Hecht opt 4e
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About This Presentation
pdf Hecht Optics 4th edition Optica de Hecht en inglés
Slide Content
International Edition
OPTICS
.
—
—;
if
Eugene Hecht
OPTICS
.
—
—;
if
Eugene Hecht
LEOPTICS
Eugene Hecht
‘Adelphi University
Eugene Hecht
‘Adelphi University
ret Manager Ney Ger
‘antag Supenor Kan MDa
ren Sonic AS tract
hot Reseach Carin Een Meck
are ht it has ben ongflly impone witout the approval ofthe Publisher
Copyright 0302 Pearson Eton Inc poling a Adlon Wes 1901
Senne St San Fan, CA 9111 Alsip senos Manuel ine
Usted Sits Ameri, Tis plication proeed by Copyright and pe
sete td fo he per port ods
$c elf i a an AN LP
pain ac he dv nn pn
A
w
idison
Wesley 123456789 10-MA-a4oa 201
‘antag Supenor Kan MDa
ren Sonic AS tract
hot Reseach Carin Een Meck
are ht it has ben ongflly impone witout the approval ofthe Publisher
Copyright 0302 Pearson Eton Inc poling a Adlon Wes 1901
Senne St San Fan, CA 9111 Alsip senos Manuel ine
Usted Sits Ameri, Tis plication proeed by Copyright and pe
sete td fo he per port ods
$c elf i a an AN LP
pain ac he dv nn pn
A
w
idison
Wesley 123456789 10-MA-a4oa 201
Preface
To Ca, b.ww.d.
À ven
Hide By tice dit imperaives to ic-tune the pe
ey, modemize ie discos, and update the content
During ie pas ver sar, using ie id ein ia he
inseroom, a number of smal ut significant pedagogical
reiement ave evoed, and ee have hen PA
"ghoul hs vie text, Fa stance al symbol pre
senting vectors now have an arrow deci above them. The
nena ever isto be responsive to student ped
Thi ein continues te program of gral modemiz-
ingle resumen In th, there ae several gal, victor the
catering in almost every aspect of Optics provide an
ledersanding, as cal s possible, ofthe insight pere
{ve are by Fourier Theory and o make cleat. fom the
Tecinologcl advances have sen mude na wie range of
areas rom eee and aserto ekescapes an ites Tis
{ou ein mes ven sometimes oni im nado
sould be aware of.
“Ate request of users, have added doves of new prob
fem throughout the tt. Most of these were designed o
develop needed analytics nd ar ofthe as trier
ed” ai. Asn previous cios, the complete sos
ebook. sal be noted hs he sat majority ofthe ne
problems ar not provided vá such solutions, This was done
15 etease the selection of pote homework questions
Much fort was expended in redrawin well vera han
‘et pieces of existing at to make them clearer andthe
‘ysis more ele To fuer canos the pedago, hi
‘ton also contains many new drawings and photographs
‘Chapter 2 (Wave Motion), which as ie mathematical
groundwork or wave hey, has ben somewhat reed in
‘eer both o make he existing material lester and provide
sonde oundton fr whats to some. Fr instance the di
sion ofthe differential wave equation (p. 13) hasbeen
‘eed ata it, with same ofthe previously sing eps
ow provided
us boon extensively reworked. Nowadays many students
studying Opis come tot with ile more than the bri np
Sure to elecvomagnetic theory afforded bythe tada!
Basic Laws of Electromagnetic They (p 37, hs been
‘expanded, making the material ar more accesible o these
Students. a kecping wi he commento discuss modem
anplcaions of Ops anew secon called Optical Cooling
naines his important technique (p. 6)
The Propagation of Ligh (Chapter 3) pow coin a di
‘cussion ofthe historical origins ofthe concep of nd of
refraction (88). This helps to make Small à Law eae to
tall understand. The chapters further nance wi a more
thorough eme of Fermat and Mirages (p. 107) A nee
section, 3.12 called Photons ond the Lv Reflection ná
Refraction (p.141 completes the chop,
The weriment of Geometrical Opie (Chapter 8) wat
sein here and there (pp 161, 1, 166, 178 and 215)
o improve is lay, The Nela of lecommuncalions o.
important and so rapid evolving tat each ein o this
book has ad 0 ea several major echologea Vas.
Accodngly. he discusion a bropics was rough pt
dite withthe consideration of such fps ax eh doped
To Ca, b.ww.d.
À ven
Hide By tice dit imperaives to ic-tune the pe
ey, modemize ie discos, and update the content
During ie pas ver sar, using ie id ein ia he
inseroom, a number of smal ut significant pedagogical
reiement ave evoed, and ee have hen PA
"ghoul hs vie text, Fa stance al symbol pre
senting vectors now have an arrow deci above them. The
nena ever isto be responsive to student ped
Thi ein continues te program of gral modemiz-
ingle resumen In th, there ae several gal, victor the
catering in almost every aspect of Optics provide an
ledersanding, as cal s possible, ofthe insight pere
{ve are by Fourier Theory and o make cleat. fom the
Tecinologcl advances have sen mude na wie range of
areas rom eee and aserto ekescapes an ites Tis
{ou ein mes ven sometimes oni im nado
sould be aware of.
“Ate request of users, have added doves of new prob
fem throughout the tt. Most of these were designed o
develop needed analytics nd ar ofthe as trier
ed” ai. Asn previous cios, the complete sos
ebook. sal be noted hs he sat majority ofthe ne
problems ar not provided vá such solutions, This was done
15 etease the selection of pote homework questions
Much fort was expended in redrawin well vera han
‘et pieces of existing at to make them clearer andthe
‘ysis more ele To fuer canos the pedago, hi
‘ton also contains many new drawings and photographs
‘Chapter 2 (Wave Motion), which as ie mathematical
groundwork or wave hey, has ben somewhat reed in
‘eer both o make he existing material lester and provide
sonde oundton fr whats to some. Fr instance the di
sion ofthe differential wave equation (p. 13) hasbeen
‘eed ata it, with same ofthe previously sing eps
ow provided
us boon extensively reworked. Nowadays many students
studying Opis come tot with ile more than the bri np
Sure to elecvomagnetic theory afforded bythe tada!
Basic Laws of Electromagnetic They (p 37, hs been
‘expanded, making the material ar more accesible o these
Students. a kecping wi he commento discuss modem
anplcaions of Ops anew secon called Optical Cooling
naines his important technique (p. 6)
The Propagation of Ligh (Chapter 3) pow coin a di
‘cussion ofthe historical origins ofthe concep of nd of
refraction (88). This helps to make Small à Law eae to
tall understand. The chapters further nance wi a more
thorough eme of Fermat and Mirages (p. 107) A nee
section, 3.12 called Photons ond the Lv Reflection ná
Refraction (p.141 completes the chop,
The weriment of Geometrical Opie (Chapter 8) wat
sein here and there (pp 161, 1, 166, 178 and 215)
o improve is lay, The Nela of lecommuncalions o.
important and so rapid evolving tat each ein o this
book has ad 0 ea several major echologea Vas.
Accodngly. he discusion a bropics was rough pt
dite withthe consideration of such fps ax eh doped
he Pre
‘bec amplifier (p. 197, wavelength division molplexing,
an optical sitchin via MOEMS (. 200). Liquid mors re
rey considered on page 22. The chapter ends with a new
ston on Gravitational Lenin p.230)
"The icon of wavefront aerators in Chapter 6 Mare
‘on Geomerica Optics as becn enlarge (p.254). There à
new piece concerning the upgraded Arecibo Observatory (p.
258) boca banal stats an important cotempo
‘ary approach o dealing with sphncal aberration.
Chapter 7 (The Superpoinen of Waves) was reworked to
sake the material general more accesible (eg. . 203), The
Pan representation was wed to uminat he creation of
th standing waves (p. 288) and para tanding ave p.
239). Because ofa very significar series of experiments pub.
lished ia the ast several yeas, the discussion of Group Vel
‘typ. 296), Seton 1.22, was enriched and new succion
on Spertamina and Sublumina Light were add.
in Chapter (Polarization), as elsewhere, he prose was
sine andthe analysis clarified hee and hee. A few new
‘Photograph and several fresh diagrams were included. The
Seton (8.2) on Retrders was extended, and the concepts of
co ordered, multiple ordered and compound zero-order
(812) was added, and he operation o ach te liquid cesa
variable stander and Liquid crystal display (LCD) were
In addon few new photos and the ocasional any
ing remark, Chapter 9 (Interference now contains a vi,
984 called Radar Itereromery
“Over thet two decades here's been some interesting
‘work done on so-called nondifrcing beams. According
{Chapter 10 Difraction) contains anew son (1027) et
ted The Zero Order Bestel Beam, tha das with the pe
Chipes 11 (Fourier Opis) and 12 Basics of Coherence
Theor) hav undergone line by tine fin ting bu ite or
no over,
Chapter 3, Modern Opis: Lasers and Other Topics hos
been revised with he addition ly subrection on Gauerar
Faserbeams and some updating as required (eg. now
inclales material o he Ome se)
This fourth edition continue the agenda of unifying the
scours as muchas posible, win the framework fen.
ran ides. Thus the concept of mtrfrene, wich sone of
{he premier notion in Opies (and not surprisingly in Qua
tum Mechanics, as wel is wed qualcively to understand
propagation phenomena ong bfor its studied formally in
{Chapter 9. Among ther benefis, ths approach of presenting
‘vanced conceps in simplified form eal athe exposition
Slows the student develop a eabesive perspective,
(Over he years, have recived comments ticles, and
hotograps, rom hundreds o eallesgues, and mos incre
Iythank them all Lam especially pratefulto Professor
Jacksonville University, M. W. Coffey ofthe University of
Colorado and H, Feam of Califom Sate Unversity lo ir
contributions and suggestions. Prof. J. R.Peverley of The
George Washington Unveriy kindy dated several very.
ce problems on Jones mate and an him or helping o
be ap tis sil. Anyone le wising io combate
their fave problems, pease fl eto do dec you
are interested in the discipline und wish to exchange ideas you
fn contact me by mui Adelphi Unie, Physics Depa
tment, Garden Cy, NY. 11930 or at genehecht@ aol.com,
Tike eo thank the entre team at Addon Wesley, oral
hei help. without which this edition would never have seen
the light of day sk wer. Tam especially grateful to Adam
Black who enbusism forthe project was sustaimin 0
Joan Mart whe wise dernions nade he whole thing man
ageable, ando Nancy Gee who handle he da-to-da ope
ston with eficeny and god humor
The book was produced by HRS Interactive, which dida
brian jb of geting all together Lorraine Burke watched
‘over etry aspect of he process with increible paieso and
Skill Alan Wiener and Jennifer Burke ceefully router
production acumen 10 bear Ed Burke designed a beautiful
Deck and struggled igi to maitin the highest standards;
Hilda Espr mas the Giles composi: and as exer Pat
FHamagan, with he able asistan of Chis Burke, produced
incomparable an. Al have my deepest respect und profound
spprecation. Finally, 1 tank my dear fend, my sie,
Carolyn Eisen Hecht for coping wh one more ein fo.
‘more book,
Freeport, New York En
‘bec amplifier (p. 197, wavelength division molplexing,
an optical sitchin via MOEMS (. 200). Liquid mors re
rey considered on page 22. The chapter ends with a new
ston on Gravitational Lenin p.230)
"The icon of wavefront aerators in Chapter 6 Mare
‘on Geomerica Optics as becn enlarge (p.254). There à
new piece concerning the upgraded Arecibo Observatory (p.
258) boca banal stats an important cotempo
‘ary approach o dealing with sphncal aberration.
Chapter 7 (The Superpoinen of Waves) was reworked to
sake the material general more accesible (eg. . 203), The
Pan representation was wed to uminat he creation of
th standing waves (p. 288) and para tanding ave p.
239). Because ofa very significar series of experiments pub.
lished ia the ast several yeas, the discussion of Group Vel
‘typ. 296), Seton 1.22, was enriched and new succion
on Spertamina and Sublumina Light were add.
in Chapter (Polarization), as elsewhere, he prose was
sine andthe analysis clarified hee and hee. A few new
‘Photograph and several fresh diagrams were included. The
Seton (8.2) on Retrders was extended, and the concepts of
co ordered, multiple ordered and compound zero-order
(812) was added, and he operation o ach te liquid cesa
variable stander and Liquid crystal display (LCD) were
In addon few new photos and the ocasional any
ing remark, Chapter 9 (Interference now contains a vi,
984 called Radar Itereromery
“Over thet two decades here's been some interesting
‘work done on so-called nondifrcing beams. According
{Chapter 10 Difraction) contains anew son (1027) et
ted The Zero Order Bestel Beam, tha das with the pe
Chipes 11 (Fourier Opis) and 12 Basics of Coherence
Theor) hav undergone line by tine fin ting bu ite or
no over,
Chapter 3, Modern Opis: Lasers and Other Topics hos
been revised with he addition ly subrection on Gauerar
Faserbeams and some updating as required (eg. now
inclales material o he Ome se)
This fourth edition continue the agenda of unifying the
scours as muchas posible, win the framework fen.
ran ides. Thus the concept of mtrfrene, wich sone of
{he premier notion in Opies (and not surprisingly in Qua
tum Mechanics, as wel is wed qualcively to understand
propagation phenomena ong bfor its studied formally in
{Chapter 9. Among ther benefis, ths approach of presenting
‘vanced conceps in simplified form eal athe exposition
Slows the student develop a eabesive perspective,
(Over he years, have recived comments ticles, and
hotograps, rom hundreds o eallesgues, and mos incre
Iythank them all Lam especially pratefulto Professor
Jacksonville University, M. W. Coffey ofthe University of
Colorado and H, Feam of Califom Sate Unversity lo ir
contributions and suggestions. Prof. J. R.Peverley of The
George Washington Unveriy kindy dated several very.
ce problems on Jones mate and an him or helping o
be ap tis sil. Anyone le wising io combate
their fave problems, pease fl eto do dec you
are interested in the discipline und wish to exchange ideas you
fn contact me by mui Adelphi Unie, Physics Depa
tment, Garden Cy, NY. 11930 or at genehecht@ aol.com,
Tike eo thank the entre team at Addon Wesley, oral
hei help. without which this edition would never have seen
the light of day sk wer. Tam especially grateful to Adam
Black who enbusism forthe project was sustaimin 0
Joan Mart whe wise dernions nade he whole thing man
ageable, ando Nancy Gee who handle he da-to-da ope
ston with eficeny and god humor
The book was produced by HRS Interactive, which dida
brian jb of geting all together Lorraine Burke watched
‘over etry aspect of he process with increible paieso and
Skill Alan Wiener and Jennifer Burke ceefully router
production acumen 10 bear Ed Burke designed a beautiful
Deck and struggled igi to maitin the highest standards;
Hilda Espr mas the Giles composi: and as exer Pat
FHamagan, with he able asistan of Chis Burke, produced
incomparable an. Al have my deepest respect und profound
spprecation. Finally, 1 tank my dear fend, my sie,
Carolyn Eisen Hecht for coping wh one more ein fo.
‘more book,
Freeport, New York En
Content
1A Brief History 1
1.1. Prolegomenon 1
12. Inthe Beginning 1
13. From the Seventeenth Century 2
14 The Nineteenth Century 4
LS Tuenteth Century Optics 7
2 Wave Motion 10
21 One Dimension Waves 10
22 Harmonic Waves 14
23 Phase and Phase Velocity 17
24 The Superpostion Principle 20
25 The Complex Representation 21
26 Phasors and the Addition of Waves 23
27 Plane Waves 24
2.8 The Three Dimensional Difeenta
Wave Equation 27
29 Spherical Waves 28
210 Cylindrical Waves 31
Problems 32
3 Electromagnetic Theory, Photons,
and Light 36
3.1. Basic Laws of Electromagnetic Theory 37
32 Electromagnetic Waves 44
33 Energy and Momentum 47
34 Radiation 58
33 Lightin Buk Matter 66
36. The ElecvomagneticPhoton Spectrum 73
37 Quantum Feld Theory 80
Problems 82
4 The Propagation of Light 86
‘41 Introduction 86
42
44
45
46
47
48
49
10
au
Rayleigh Scattering 86
Reflection 95
Refraction 100
Fermats Principle 106
The Electromagnetic Approach 111
Total internal election 122
Optical Properties of Metals 127
Famiba Aspects ofthe Interaction of
Light and Mater 131
The Stokes Treatment of Reflection and
Refraction 136
Photons, Waves, and Probabity 137.
Problems 141
5 Geometrical Optics 149
51
52
53
54
55
56
57
58
59
Introductory Remarks 149
Lenses 150
Stops 172
Mirrors 175
Prisms 186
Fiberoptes 193
Optical Systems 201
Wavefront Sheping 226
Gravitation Lensing 231
Problems 234
6 More on Geometrical Optics 243
si
62
sa
64
ss
Thick Lenses and Lens Systems 243
AnalficalRay Tracing 246
Aberrations 253
GRIN Systems 273
Concluding Remarks 276
Problems 277
1A Brief History 1
1.1. Prolegomenon 1
12. Inthe Beginning 1
13. From the Seventeenth Century 2
14 The Nineteenth Century 4
LS Tuenteth Century Optics 7
2 Wave Motion 10
21 One Dimension Waves 10
22 Harmonic Waves 14
23 Phase and Phase Velocity 17
24 The Superpostion Principle 20
25 The Complex Representation 21
26 Phasors and the Addition of Waves 23
27 Plane Waves 24
2.8 The Three Dimensional Difeenta
Wave Equation 27
29 Spherical Waves 28
210 Cylindrical Waves 31
Problems 32
3 Electromagnetic Theory, Photons,
and Light 36
3.1. Basic Laws of Electromagnetic Theory 37
32 Electromagnetic Waves 44
33 Energy and Momentum 47
34 Radiation 58
33 Lightin Buk Matter 66
36. The ElecvomagneticPhoton Spectrum 73
37 Quantum Feld Theory 80
Problems 82
4 The Propagation of Light 86
‘41 Introduction 86
42
44
45
46
47
48
49
10
au
Rayleigh Scattering 86
Reflection 95
Refraction 100
Fermats Principle 106
The Electromagnetic Approach 111
Total internal election 122
Optical Properties of Metals 127
Famiba Aspects ofthe Interaction of
Light and Mater 131
The Stokes Treatment of Reflection and
Refraction 136
Photons, Waves, and Probabity 137.
Problems 141
5 Geometrical Optics 149
51
52
53
54
55
56
57
58
59
Introductory Remarks 149
Lenses 150
Stops 172
Mirrors 175
Prisms 186
Fiberoptes 193
Optical Systems 201
Wavefront Sheping 226
Gravitation Lensing 231
Problems 234
6 More on Geometrical Optics 243
si
62
sa
64
ss
Thick Lenses and Lens Systems 243
AnalficalRay Tracing 246
Aberrations 253
GRIN Systems 273
Concluding Remarks 276
Problems 277
7 The Superposition of
Waves 281
7.1. The Addtion of Waves of the Same
Frequency 282
7.2 The Addtion of Waves of Different
Frequency 294
7.3 Anharmonic Period: Waves 302
7.4 Nonperiod Waves 308
Problems. 320.
8 Polarization 325
81. The Natur of Polarized Light 325
82 Polaizers 331
83 Dichroism 333
84 Birefingence 336
85 Scattering and Polarization 344
86 Polarization by Reflection 348
87 Retaders 352
88 CrcularPolezers 357
8.9. Polarization of Pobchromai Light 358
819 Optical Activity. 360:
8.11 Induced Optica Etfects—Optical
Modulators 365
8.12 Liquid Cystls 370
8.13 AMathematical Description of
Polarization 372
Problems 379
9 Interference 385
91 General Considerations 386
9.2 Conditions for Intererence 390
9.3 Wavelontspltting interferometers 393
94 Ampitudesplting interferometers 400
9.5 Types and Localization of Interference
Fringes 414
9.6 MattpleBeam interference 416
9.7. Aoplcations of Single and Mutiayer
Fins 425
9.8 Applications of nerferometry 431
Problems _ 438
10 Diffraction 443
10.1 Preliminary Considerations 443
10.2 Fraunhofer Ditraction 452
103 FresnelDifracton 485
10.4 Krehhoffs ScalarDifraction Theory 510
105 BoundaryDifracton Waves 512
Probloms 514
11 Fourier Optics 519
ALA introduction 519
112 Fourier Trenstorms 519
113 Optical Applications 529
Problems 556
12 Basics of Coherence
Theory 560
121 Introduction 560
122 Visbiity 562
1233. The Mutual Coherence Function and the
Degree of Coherence 565,
124 Coherence and Stelarltererometry 573
Problems 578
13 Modern Optics: Lasers and
Other Topics 581
131 Lasers and Laseright 581
13.2 imagery — The Spatial Distribution of
Optical Information 606
13.3 Holography 623
134 Novinear Opies 639
Problems 644
‘Appendix 1 649
Appendix 2 652
Table1 653
Solutions to Selected Problems 658
Bibliography 685
index 689
Waves 281
7.1. The Addtion of Waves of the Same
Frequency 282
7.2 The Addtion of Waves of Different
Frequency 294
7.3 Anharmonic Period: Waves 302
7.4 Nonperiod Waves 308
Problems. 320.
8 Polarization 325
81. The Natur of Polarized Light 325
82 Polaizers 331
83 Dichroism 333
84 Birefingence 336
85 Scattering and Polarization 344
86 Polarization by Reflection 348
87 Retaders 352
88 CrcularPolezers 357
8.9. Polarization of Pobchromai Light 358
819 Optical Activity. 360:
8.11 Induced Optica Etfects—Optical
Modulators 365
8.12 Liquid Cystls 370
8.13 AMathematical Description of
Polarization 372
Problems 379
9 Interference 385
91 General Considerations 386
9.2 Conditions for Intererence 390
9.3 Wavelontspltting interferometers 393
94 Ampitudesplting interferometers 400
9.5 Types and Localization of Interference
Fringes 414
9.6 MattpleBeam interference 416
9.7. Aoplcations of Single and Mutiayer
Fins 425
9.8 Applications of nerferometry 431
Problems _ 438
10 Diffraction 443
10.1 Preliminary Considerations 443
10.2 Fraunhofer Ditraction 452
103 FresnelDifracton 485
10.4 Krehhoffs ScalarDifraction Theory 510
105 BoundaryDifracton Waves 512
Probloms 514
11 Fourier Optics 519
ALA introduction 519
112 Fourier Trenstorms 519
113 Optical Applications 529
Problems 556
12 Basics of Coherence
Theory 560
121 Introduction 560
122 Visbiity 562
1233. The Mutual Coherence Function and the
Degree of Coherence 565,
124 Coherence and Stelarltererometry 573
Problems 578
13 Modern Optics: Lasers and
Other Topics 581
131 Lasers and Laseright 581
13.2 imagery — The Spatial Distribution of
Optical Information 606
13.3 Holography 623
134 Novinear Opies 639
Problems 644
‘Appendix 1 649
Appendix 2 652
Table1 653
Solutions to Selected Problems 658
Bibliography 685
index 689
| A Brief History
1.1 Prolegomenon
mach the science of Optics, with particular emphasis on
{spt of contemporary interest The bot embraces vat
N ohne rum over soupy tye tous
crol e human cen, Before embarking on sy of the
Teds here for no Dir reason than to pt ial in
erp
12 In the Beginning
The ins o oca ecology dt ack remote aq
orange ak and tabernacle, reas "e loking ae.
mor wee made of posed copper. bone. and later ono!
pecan a copy ally ic int, Specimens ave survived
sneaked long with some tos from the workers” ater:
neath pyramid of Soon (cn, 1900 2.) ne Nile
Empedote, Plato, Anse and others developed several
theres of he ete of ig Te etlineae ropagatlon a
Tg p89) mas known, a was the La efec 9.97)
enunciated by Euclid 00) inhi book Caoprc Heo
sein hat ight averses the shortest allowed path between
‘wo pos, The burning glass (a positive lens used o start
Clouds (324 mc.) The apparent beading of objets pany
‘immersed in wate (p- 402) mentioned ia Plato's Republic
Refraction was studied by Cleomedes (SI 2.0. and ater by
Claudius iolemy (130.0) o Alexandria. who tabulated
ely precise measurement of the angles incidence and
refraction for several media (7. 101). s lear from the
also possessed buming slases. Several glass and crystal
Spheres have been found among Roman runs, and plana
‘ves lens was recovered in Pompei. The Roman pliloso-
her Seneca (3.6.65 a. pointed out tat a glass globe
it is certainly possible hat some Roman artisans may have
‘sed maine sass co facial very fine deiled work
‘wich oughly marks the str o the Dark Ages. it
Scat progres was made in Europe for a great wile. The
dominance ofthe Greeo-Roman-Chrstin cule inte lads
‘embracing the Mediterranean soon gave way by conquest 10
‘world and Optics was studied and extended especially by
Altazen ca. 1000 a.) He elaborated onthe Law of Ref
‘plane normal to the interface (p 9): he studied spherical and
fanbolic micros and gave a detailed description ofthe human
eye (p.202
"By the late par ofthe he century, Europe was oly
heginingro rouse foe ts intellectual stupor. Alhazen's mod
ings of Roben Grosses (1175-1283), Bishop of Lincoln,
‘whom were influntal in ending he study of Optics. Their
works were known tothe Franciscan Roger Bacon (1215
1298}, who i eomidere by many to be the Fst scientist in
the mem sense. He seems to have initiated the a of using
1.1 Prolegomenon
mach the science of Optics, with particular emphasis on
{spt of contemporary interest The bot embraces vat
N ohne rum over soupy tye tous
crol e human cen, Before embarking on sy of the
Teds here for no Dir reason than to pt ial in
erp
12 In the Beginning
The ins o oca ecology dt ack remote aq
orange ak and tabernacle, reas "e loking ae.
mor wee made of posed copper. bone. and later ono!
pecan a copy ally ic int, Specimens ave survived
sneaked long with some tos from the workers” ater:
neath pyramid of Soon (cn, 1900 2.) ne Nile
Empedote, Plato, Anse and others developed several
theres of he ete of ig Te etlineae ropagatlon a
Tg p89) mas known, a was the La efec 9.97)
enunciated by Euclid 00) inhi book Caoprc Heo
sein hat ight averses the shortest allowed path between
‘wo pos, The burning glass (a positive lens used o start
Clouds (324 mc.) The apparent beading of objets pany
‘immersed in wate (p- 402) mentioned ia Plato's Republic
Refraction was studied by Cleomedes (SI 2.0. and ater by
Claudius iolemy (130.0) o Alexandria. who tabulated
ely precise measurement of the angles incidence and
refraction for several media (7. 101). s lear from the
also possessed buming slases. Several glass and crystal
Spheres have been found among Roman runs, and plana
‘ves lens was recovered in Pompei. The Roman pliloso-
her Seneca (3.6.65 a. pointed out tat a glass globe
it is certainly possible hat some Roman artisans may have
‘sed maine sass co facial very fine deiled work
‘wich oughly marks the str o the Dark Ages. it
Scat progres was made in Europe for a great wile. The
dominance ofthe Greeo-Roman-Chrstin cule inte lads
‘embracing the Mediterranean soon gave way by conquest 10
‘world and Optics was studied and extended especially by
Altazen ca. 1000 a.) He elaborated onthe Law of Ref
‘plane normal to the interface (p 9): he studied spherical and
fanbolic micros and gave a detailed description ofthe human
eye (p.202
"By the late par ofthe he century, Europe was oly
heginingro rouse foe ts intellectual stupor. Alhazen's mod
ings of Roben Grosses (1175-1283), Bishop of Lincoln,
‘whom were influntal in ending he study of Optics. Their
works were known tothe Franciscan Roger Bacon (1215
1298}, who i eomidere by many to be the Fst scientist in
the mem sense. He seems to have initiated the a of using
2 Chapter Arto
Tenis for comes iin and ven hited te posa
of combining ees 1 or a espe: Ba so ad Sm
understanding of he way ln which aye raver ale. Ae
his ent, pépins Even sob he mi 3
Bumpeen pamungs were epi monks wearing ets
mercury tht was ube onto he hack ot las pits to make
tro Leonardo da Vins (4521519) deserted the cam
Yan Battista Della Porta (1535-1613). who discussed
This forthe mon par, modes aay ol ves consis
ndoubtdiy beginning bet on the wäole a bumble one
‘The whilvind of accomplishment and excitement was o
1.3 From the Seventeenth Century
inne tok dees the Sead option o eth de
familiar formation ofthe Law of Refraction in terms of
Sins: Descartes deduced the la using a model io which ight
Ie putin is Lo Dipti (1637)
The universe wats plenum, Pee de Feat (1601-1665),
taking exception to Descartes’ sumptions denied the
Law of election p. 100 from his own Princip of Leust
“Te phenomenon of dition tht ste deviation fom
tesla propagation that occurs when ligt avances
Tenis for comes iin and ven hited te posa
of combining ees 1 or a espe: Ba so ad Sm
understanding of he way ln which aye raver ale. Ae
his ent, pépins Even sob he mi 3
Bumpeen pamungs were epi monks wearing ets
mercury tht was ube onto he hack ot las pits to make
tro Leonardo da Vins (4521519) deserted the cam
Yan Battista Della Porta (1535-1613). who discussed
This forthe mon par, modes aay ol ves consis
ndoubtdiy beginning bet on the wäole a bumble one
‘The whilvind of accomplishment and excitement was o
1.3 From the Seventeenth Century
inne tok dees the Sead option o eth de
familiar formation ofthe Law of Refraction in terms of
Sins: Descartes deduced the la using a model io which ight
Ie putin is Lo Dipti (1637)
The universe wats plenum, Pee de Feat (1601-1665),
taking exception to Descartes’ sumptions denied the
Law of election p. 100 from his own Princip of Leust
“Te phenomenon of dition tht ste deviation fom
tesla propagation that occurs when ligt avances
tae en 16423727,
teyondansbstrcton (p42), was ist noted by Professor
Francesco Maria Grimald (1618-1663) the eau Cage
in Bologne. He ha oberved hands o ight within be shadow
of a rod illuminated by a small source. Robert Hooke
(1635-1709), curator of experiments forthe Royal Soviet
London ter ao observed dilación effects He ws he
To dy the lve metres pateras (. $00) ene
aed ty in film (Micrographi, 1065). He proposed he
ia hat ight as rapid vibratory motion of he medium,
"raton ole Luminous body wil generat a spree
alles death, Ina Newton (1682-1727) was bom The
thr of Newton's scene for was to bull on det
ohenaion and avoid speculative hypotheses, Taus he
eine ambivalent (ora long while bout he cial nature
‘aiid Or was ht a wave nan al penvoling medio,
ents en persion.
Newt conc twit ight was compared of ami
ue fa wae range of independent colors p. 189) He man
ind that the corals of ight social with he various
‘alors excited the see into characteristic iban: Even
though is work simulancously embraced ot he wine and
nin copula tease dl Become mar com
Aa others he grew oder. His man ron Joe
explaining clear propagation in terms of waves that
‘prea ot inal directions
trying to remove chromatic aberration from refracting tel.
‘scope lemes. Emoneouly concluding tat could nt be
done, he tomes 1 the design of electors Sr Inc’ Hit
reflecting telescope, completed in 1668, was only 6 faces.
about the same time that Newton was emphasizing De
min eo ln England Chan Huygens (1629-1055.
‘on the continent, was rent extending the wave theory
‘once hat ight effective slowed dn on entering mor
Sense media, He was able to derive the Las of Reflection aa
(9.337. mg his wave emy. Anda mile working wih
Clete at he discovered the phenomenon of parat
wo.
lation oFaıhereal mar. an cas, i was general y agreed
‘hat light propagated instantaneously, a notion that went back
teyondansbstrcton (p42), was ist noted by Professor
Francesco Maria Grimald (1618-1663) the eau Cage
in Bologne. He ha oberved hands o ight within be shadow
of a rod illuminated by a small source. Robert Hooke
(1635-1709), curator of experiments forthe Royal Soviet
London ter ao observed dilación effects He ws he
To dy the lve metres pateras (. $00) ene
aed ty in film (Micrographi, 1065). He proposed he
ia hat ight as rapid vibratory motion of he medium,
"raton ole Luminous body wil generat a spree
alles death, Ina Newton (1682-1727) was bom The
thr of Newton's scene for was to bull on det
ohenaion and avoid speculative hypotheses, Taus he
eine ambivalent (ora long while bout he cial nature
‘aiid Or was ht a wave nan al penvoling medio,
ents en persion.
Newt conc twit ight was compared of ami
ue fa wae range of independent colors p. 189) He man
ind that the corals of ight social with he various
‘alors excited the see into characteristic iban: Even
though is work simulancously embraced ot he wine and
nin copula tease dl Become mar com
Aa others he grew oder. His man ron Joe
explaining clear propagation in terms of waves that
‘prea ot inal directions
trying to remove chromatic aberration from refracting tel.
‘scope lemes. Emoneouly concluding tat could nt be
done, he tomes 1 the design of electors Sr Inc’ Hit
reflecting telescope, completed in 1668, was only 6 faces.
about the same time that Newton was emphasizing De
min eo ln England Chan Huygens (1629-1055.
‘on the continent, was rent extending the wave theory
‘once hat ight effective slowed dn on entering mor
Sense media, He was able to derive the Las of Reflection aa
(9.337. mg his wave emy. Anda mile working wih
Clete at he discovered the phenomenon of parat
wo.
lation oFaıhereal mar. an cas, i was general y agreed
‘hat light propagated instantaneously, a notion that went back
determined by the Dane Ole Cuiensen Ramer (1642
O) pi as mobo as an ak abo a pla
da ais nad ne pas of Jupes un oi ra the
‘moved hough de shadow behind Jupiter In 1676 e pri
pines as ag rome Hate speedo iat He was ale 0
penéeny estnating the Earths ora diameter. they
The reat weight of Newton's opinion hun ke astro
er the wave they ding the een centr, al bt
Ming is brocas Dest hi, he prominet mahemaicn
bie color fleets ee ina lets were set ne eye (hich
isan emunsous asumpüor) tocas te dee media ue
seat negate dispersion, He suggested that achramal eses
{bis work, Samuel Klingensjerna (1698-1765), professor at
‘Ups rpefomnes Newton's experiments on ashromatisn
and délenmeed them 1 e in eur. Klingemjeraa was in
‘Sommunicalon wäh à London optician Joh, Dollond
‘ter ft las, to form single acto ens. nin
tly, Does invenion was actualy preceded by the
1.4 The Nineteenth Century
The wave theory of igh was rebom at Le hands of Dr
"Thomas Young (1775-1825), one ofthe ly rat minds of
the Royal Society colin he wave teary and ang ot
ew funda concept the so-called Principle of Ineo
He was able to expan the colored rings o tin Mos ac
‘onceplons had tei ery origins inthe research of Newton.
he was severely tacked. ares of ate, probably
weiten by Lord Brougham. ln the Edinburgh Review
and began is biliant revival of te wave theory in
cru an he metre pei pis) The made
oF propagation oa primary wave was viewed ana ess
of sphere secondary wavelets, which ovelpped and ner
fered reorm he aan primary wave ait would appear
O) pi as mobo as an ak abo a pla
da ais nad ne pas of Jupes un oi ra the
‘moved hough de shadow behind Jupiter In 1676 e pri
pines as ag rome Hate speedo iat He was ale 0
penéeny estnating the Earths ora diameter. they
The reat weight of Newton's opinion hun ke astro
er the wave they ding the een centr, al bt
Ming is brocas Dest hi, he prominet mahemaicn
bie color fleets ee ina lets were set ne eye (hich
isan emunsous asumpüor) tocas te dee media ue
seat negate dispersion, He suggested that achramal eses
{bis work, Samuel Klingensjerna (1698-1765), professor at
‘Ups rpefomnes Newton's experiments on ashromatisn
and délenmeed them 1 e in eur. Klingemjeraa was in
‘Sommunicalon wäh à London optician Joh, Dollond
‘ter ft las, to form single acto ens. nin
tly, Does invenion was actualy preceded by the
1.4 The Nineteenth Century
The wave theory of igh was rebom at Le hands of Dr
"Thomas Young (1775-1825), one ofthe ly rat minds of
the Royal Society colin he wave teary and ang ot
ew funda concept the so-called Principle of Ineo
He was able to expan the colored rings o tin Mos ac
‘onceplons had tei ery origins inthe research of Newton.
he was severely tacked. ares of ate, probably
weiten by Lord Brougham. ln the Edinburgh Review
and began is biliant revival of te wave theory in
cru an he metre pei pis) The made
oF propagation oa primary wave was viewed ana ess
of sphere secondary wavelets, which ovelpped and ner
fered reorm he aan primary wave ait would appear
These waves were presumed to be longitudinal, in analogy
amd waves in u. reel as ae o cela te dit
{48 and satsfoctony accounts or restiincar propaga
arn hamogencosslsotople meda, thus dipeling New
{ex's main objection to the undulatry theory. When aly
‘ges Yan's ny the meee à
lin him that he was consoled by finding insel in such
[peseompanythe to great men became le,
Hagen vas amare ofthe prenomenor of portion
“sing neat crystals as was Newt. Indeed the later a
discovered that this two-sidednes flight also arose upon
reten (p38; the phenomenon wa not inherent oy
(1786-1859 hen conducted ass of experiment to deter
were uel inexplicable within the framework of hel Longs
Toi wave ptr, This was dark hor indeed For several
{sul nally Youre suggested thatthe aethereal vibration
EN e annee as va wave on sng, The two-sided
eigen stations of the seer, tansvere do the ay
‘fate scan, which edt bis now famous formulas
forte amples a rfleted and wanted igh (p13)
By 1825 the emission or corpuscular) theory had only af
reacios advocates.
‘The fin teresa determination ofthe speed of it was
eromme by Armand Hippolyte Lois Fea (1819-1895)
An 189. is apartes, consiga oli noted wheel
tnd ant miro (623 m, wa setup in suburbs of
Peis rom Suresnes o Montmare. pulse of ight leaving an
pening inthe whee struck the minor and returned. By
né e know ota! speed ofthe wel, there.
ng ul coli ma ee vo pass Era gh an opening and
Bes or1 be bret by ati Fes ave a al
Jean Bernard Léon Foucault (1819-1868) was also involved
in research on he peed af light. In 1834 Charles Whetstone
(1802-1875) had designed a ai mir rangement in
order t measure the dation a an ec par, Using hie
dense media but was never able to cary out the experiment
weal ook up he work, which as nro provide mate
A or nis doctoral mess On May 6 1850. heran me.
‘Academy of Sciences hat the speed light water was eur
than thal in air. This remit was in cet cont with New
tons formulatio of te omiso theory and hard bow to
few remaining devotes.
Wie af this was happesing in Optic, quite indepen
cole sudyafelecuichy and menti nas also hear
ing min 1885 the master experimental Michael Faatay
(791-1867 esabihed an terre ail between lero
sente ad ish when he found athe poration die
tf ham Cd aed yong mga à
balan summarized and extended al th empirical kn
pe onthe subject in a gle set of mathematical equations
‘Begining with bis emarkahysucinct and Beauly yey
metrical satis, he was able to sho, purely theoreti
that the elecwomagnei eld could propage a wansvene
wave inthe miners setter. 4)
Solving for the sped ofthe wave, Maxwell assed a an
expression inte of elect and magnetic propenie othe
ve Cr Mae 851
amd waves in u. reel as ae o cela te dit
{48 and satsfoctony accounts or restiincar propaga
arn hamogencosslsotople meda, thus dipeling New
{ex's main objection to the undulatry theory. When aly
‘ges Yan's ny the meee à
lin him that he was consoled by finding insel in such
[peseompanythe to great men became le,
Hagen vas amare ofthe prenomenor of portion
“sing neat crystals as was Newt. Indeed the later a
discovered that this two-sidednes flight also arose upon
reten (p38; the phenomenon wa not inherent oy
(1786-1859 hen conducted ass of experiment to deter
were uel inexplicable within the framework of hel Longs
Toi wave ptr, This was dark hor indeed For several
{sul nally Youre suggested thatthe aethereal vibration
EN e annee as va wave on sng, The two-sided
eigen stations of the seer, tansvere do the ay
‘fate scan, which edt bis now famous formulas
forte amples a rfleted and wanted igh (p13)
By 1825 the emission or corpuscular) theory had only af
reacios advocates.
‘The fin teresa determination ofthe speed of it was
eromme by Armand Hippolyte Lois Fea (1819-1895)
An 189. is apartes, consiga oli noted wheel
tnd ant miro (623 m, wa setup in suburbs of
Peis rom Suresnes o Montmare. pulse of ight leaving an
pening inthe whee struck the minor and returned. By
né e know ota! speed ofthe wel, there.
ng ul coli ma ee vo pass Era gh an opening and
Bes or1 be bret by ati Fes ave a al
Jean Bernard Léon Foucault (1819-1868) was also involved
in research on he peed af light. In 1834 Charles Whetstone
(1802-1875) had designed a ai mir rangement in
order t measure the dation a an ec par, Using hie
dense media but was never able to cary out the experiment
weal ook up he work, which as nro provide mate
A or nis doctoral mess On May 6 1850. heran me.
‘Academy of Sciences hat the speed light water was eur
than thal in air. This remit was in cet cont with New
tons formulatio of te omiso theory and hard bow to
few remaining devotes.
Wie af this was happesing in Optic, quite indepen
cole sudyafelecuichy and menti nas also hear
ing min 1885 the master experimental Michael Faatay
(791-1867 esabihed an terre ail between lero
sente ad ish when he found athe poration die
tf ham Cd aed yong mga à
balan summarized and extended al th empirical kn
pe onthe subject in a gle set of mathematical equations
‘Begining with bis emarkahysucinct and Beauly yey
metrical satis, he was able to sho, purely theoreti
that the elecwomagnei eld could propage a wansvene
wave inthe miners setter. 4)
Solving for the sped ofthe wave, Maxwell assed a an
expression inte of elect and magnetic propenie othe
ve Cr Mae 851
6 por Aba
made = VUN i. Upon subie konn ein
y dtemined values or these quan, he obtained mum
ital reall qual tothe measured speed of ph The
father. Manuel ded athe age Ach yeas oo soon
er the experimental confirmation Singes ant rt
soon for pays Henn Aut Herts (2857-1855) ered
ne xeme of long eleetomagnetic waves by genesis and
‘yading substratum the huminiferows acther. If here were
axes serie oUF ac er MU De à ONE
‘neu Que atra. reat dea of enc effort went
lao eel te gsc nature ofthe ater, eto
Bern lw an amor epee tna a cece
"bodies Atte same tine, could spore exceedingly
highnroquency (10° Hz) oscilan ol gh tavelig at
resoring orcos within the ethereal substance, The sped at
Which wave advance rough a edi dependen onthe
‘harctersics ol te dute sahtralum and aot on any
tition f the sa Ti sim contrast foe Behavior oa
the essential parameter
Conan pacte af tt father inde when stay
ext great meng point In 1725 James Bradley (1693-1762
then Savlan Profesor of Aston at Onfonl, temple a
to different times of he year. The position 0! the Far
are asie or Glangultion ox de sr, To sarro
Fale found tn “ise” sas displayed an apparent pe
tema movement related othe drin ol mation e he
anh cai and no dependen, shad Been anipted. on
‘he Ears positon a pace Tl would ear aberration
is analog to eve own ali cido Susi. A
‘aindop.alhovgh tevin serially with respect lo a.
‘lof igh cold epli sll aherain ter andi, Aer
Earth pons though
through te acter might resul in an observable erence
beten ight rom etl ad xls sures, A
‘atthe were ao such iservabe differences Lit tanos
ust at if the Earth were at ea with respect ih acer. To
plan bes resus, Free sue ih eet tha ight was
paria dragged along savers aransaret miam in
‘oto, Experiments by Fizea,n which ight beats pas
[Ai (0801-1892), bo ed a water led telescope in 1571
o examine stellar aberration, both seemed to confirm Free
Hendrik Antoon Lorentz (1553-1928) derived theory thal
Almanac Office, Maxwell suggested a scheme for measuring
ine determination ofthe speed of ight. A few year ater be
sonar nage ter Since he pee of it in eter
start andthe Eat, nur, presumably moves in elation
tobe aıher (il speed of 67000 1/1), speedo ight
pants maton. ln TRE he published his idigs Tete was
ie ter was tony Butte deivere of his up
ing rer was led some ar wen Lorenz pones out
the profesor of pss at Cae Se App Scene in
Cleveland. Ohio, joined with Edvard Wins Morey
Reserve, to redo the experiment with considerably greater pre
‘son, Amarinply enough, her ests, plished in 1097
made = VUN i. Upon subie konn ein
y dtemined values or these quan, he obtained mum
ital reall qual tothe measured speed of ph The
father. Manuel ded athe age Ach yeas oo soon
er the experimental confirmation Singes ant rt
soon for pays Henn Aut Herts (2857-1855) ered
ne xeme of long eleetomagnetic waves by genesis and
‘yading substratum the huminiferows acther. If here were
axes serie oUF ac er MU De à ONE
‘neu Que atra. reat dea of enc effort went
lao eel te gsc nature ofthe ater, eto
Bern lw an amor epee tna a cece
"bodies Atte same tine, could spore exceedingly
highnroquency (10° Hz) oscilan ol gh tavelig at
resoring orcos within the ethereal substance, The sped at
Which wave advance rough a edi dependen onthe
‘harctersics ol te dute sahtralum and aot on any
tition f the sa Ti sim contrast foe Behavior oa
the essential parameter
Conan pacte af tt father inde when stay
ext great meng point In 1725 James Bradley (1693-1762
then Savlan Profesor of Aston at Onfonl, temple a
to different times of he year. The position 0! the Far
are asie or Glangultion ox de sr, To sarro
Fale found tn “ise” sas displayed an apparent pe
tema movement related othe drin ol mation e he
anh cai and no dependen, shad Been anipted. on
‘he Ears positon a pace Tl would ear aberration
is analog to eve own ali cido Susi. A
‘aindop.alhovgh tevin serially with respect lo a.
‘lof igh cold epli sll aherain ter andi, Aer
Earth pons though
through te acter might resul in an observable erence
beten ight rom etl ad xls sures, A
‘atthe were ao such iservabe differences Lit tanos
ust at if the Earth were at ea with respect ih acer. To
plan bes resus, Free sue ih eet tha ight was
paria dragged along savers aransaret miam in
‘oto, Experiments by Fizea,n which ight beats pas
[Ai (0801-1892), bo ed a water led telescope in 1571
o examine stellar aberration, both seemed to confirm Free
Hendrik Antoon Lorentz (1553-1928) derived theory thal
Almanac Office, Maxwell suggested a scheme for measuring
ine determination ofthe speed of ight. A few year ater be
sonar nage ter Since he pee of it in eter
start andthe Eat, nur, presumably moves in elation
tobe aıher (il speed of 67000 1/1), speedo ight
pants maton. ln TRE he published his idigs Tete was
ie ter was tony Butte deivere of his up
ing rer was led some ar wen Lorenz pones out
the profesor of pss at Cae Se App Scene in
Cleveland. Ohio, joined with Edvard Wins Morey
Reserve, to redo the experiment with considerably greater pre
‘son, Amarinply enough, her ests, plished in 1097
‘Tas, whereas an explanation of el aber wii the
comet ofthe wave theory rege he cxistence ol altivo
Experiment ead that possi, Moreover, indias of
usw ná Any necessite the incio of part dsg of
igh deo main ofthe medi
1.5 Twentieth-Century Optics
Jules Hen Poincaré (1854-1912) was perhaps the irs io
asp te significance o the experiment ab 1 obseve
tomake bis vis Known, and in 1900 bes
In 1905 Alen Einstein (1879-1955) au his Special
Theory of Relativo, in which e too, quite independent
ret theater hypothesis
pen ancha tn vie fee ob eloped il
‘fone poste:
ere then explind quite natural within the framework of
Ets reviste kinemaic.» Deprived ofthe aer.
lyst py had to get ured othe idea tat coma
live Light was now envisaged sa saine ave
the concep emphasis pasing fomaetrto il. The
crane wave became sn ely IE
‘On October 19, 1900, Max Kar Emst Ladwir Planck
1858-1087) rad a paper before e German Physical Sockey
wich ie nvducod the hesitant Degimings of what waste
com ye another great revolution ln sien tought
‘Quon Mechanics a hear embracing Sbmicroop pe
la ar, Set Raat by Fa Dt
Ae ren 1679-1965
nomena (p. SO 1905, boldly building on these des in
"ein proposed a new form of corpussiar theory in which he
asser that ight onsite a lbs or “prices of energy.
‘Each such quantum of aint energy option. ait to
be ale, had an energy proporiona o ryueney ht,
{= hey whee A knows Plan a constant Fg. 1.1). By
eiseubery Schrdinger, De Broglie, Paul, Dirac and others.
(Quant Meta had hecam à weil vriied theory I
gradual became evden that the concepts of patie und
re uhich In the meme wor sect se tion
oman, The mental imaye of an omic parle (e elec
tons and neurons) as a minute localized Jump of mater
‘eon no longer sie Indeed, wa found ta ese par
precisely ame way a woul php. 399) Th photons
Protons, electron, neutrons. and so fanb-—the whole lot,
have both panico and wave manifestations, Sil the mar
rows what photon” wrote Fase. "1 pont my he 0
Relavity Hberate ight rom the ether and showed the
seemed o be two alos amic! Guanes now Besame
inerehangeable Quant Mechanics et onto eal hat
comet ofthe wave theory rege he cxistence ol altivo
Experiment ead that possi, Moreover, indias of
usw ná Any necessite the incio of part dsg of
igh deo main ofthe medi
1.5 Twentieth-Century Optics
Jules Hen Poincaré (1854-1912) was perhaps the irs io
asp te significance o the experiment ab 1 obseve
tomake bis vis Known, and in 1900 bes
In 1905 Alen Einstein (1879-1955) au his Special
Theory of Relativo, in which e too, quite independent
ret theater hypothesis
pen ancha tn vie fee ob eloped il
‘fone poste:
ere then explind quite natural within the framework of
Ets reviste kinemaic.» Deprived ofthe aer.
lyst py had to get ured othe idea tat coma
live Light was now envisaged sa saine ave
the concep emphasis pasing fomaetrto il. The
crane wave became sn ely IE
‘On October 19, 1900, Max Kar Emst Ladwir Planck
1858-1087) rad a paper before e German Physical Sockey
wich ie nvducod the hesitant Degimings of what waste
com ye another great revolution ln sien tought
‘Quon Mechanics a hear embracing Sbmicroop pe
la ar, Set Raat by Fa Dt
Ae ren 1679-1965
nomena (p. SO 1905, boldly building on these des in
"ein proposed a new form of corpussiar theory in which he
asser that ight onsite a lbs or “prices of energy.
‘Each such quantum of aint energy option. ait to
be ale, had an energy proporiona o ryueney ht,
{= hey whee A knows Plan a constant Fg. 1.1). By
eiseubery Schrdinger, De Broglie, Paul, Dirac and others.
(Quant Meta had hecam à weil vriied theory I
gradual became evden that the concepts of patie und
re uhich In the meme wor sect se tion
oman, The mental imaye of an omic parle (e elec
tons and neurons) as a minute localized Jump of mater
‘eon no longer sie Indeed, wa found ta ese par
precisely ame way a woul php. 399) Th photons
Protons, electron, neutrons. and so fanb-—the whole lot,
have both panico and wave manifestations, Sil the mar
rows what photon” wrote Fase. "1 pont my he 0
Relavity Hberate ight rom the ether and showed the
seemed o be two alos amic! Guanes now Besame
inerehangeable Quant Mechanics et onto eal hat
mor AB oy
a panico? of momentum p had an associated wavelength À
ing er rest mass, was pole for theoretical reasons
in 1980 by Wolfgang Pal (1900-1958) and verified expe
mental In the 1950s The easy images of subicroscopic
{peeks of mer became untenable, and the wave-pertil
‘Quantum Mechanics also eas th manner in which ight
jsabsorbed and erated by ator (p. ©) Sapte we aura
as to glow by heating ior passing an electrical discharge
"heh it The Lg emited charter of the very sive
ture ofthe atoms coming the pas. Spectroscopy. which is
the branch of Optics dealing with spect analysis (. 73,
developed from the research of Newton. Walia Hyde
‘Wollaston (1765-1828) made the erst observations of he
dark ines nthe solar spectram (802). Because ol he sl
Shaped aprtre generally used in specrocopes, the output
conn a core ond El Messe
AS
NE
(0747-1826 ei extended he tjs, Ar achemaly
‘ny sang and made he fr wavelength eventos
{ing din pangs 9.276) Dosis Robert Kiet
Uiticiser and Rote Wilhelm Bunsen C8t1-180)
Serine together at Nee er, stabbed that cach in of
is. Andin 191 ei Henrik aid Boh ARS ID se
specu. Te Em yan som snow understood
bain of modem quantum theory, which desebes the most
nad wi ropero a ben.
The fomi of applied Opus and tal e
aera enges un nights of comicos
ry Jus the er of omer provides ener mesi
ich sulin pecs of mean hecameprospe
Ga Femelle ve serias brad
ae opal phones Bound jeer y ke mabe
a panico? of momentum p had an associated wavelength À
ing er rest mass, was pole for theoretical reasons
in 1980 by Wolfgang Pal (1900-1958) and verified expe
mental In the 1950s The easy images of subicroscopic
{peeks of mer became untenable, and the wave-pertil
‘Quantum Mechanics also eas th manner in which ight
jsabsorbed and erated by ator (p. ©) Sapte we aura
as to glow by heating ior passing an electrical discharge
"heh it The Lg emited charter of the very sive
ture ofthe atoms coming the pas. Spectroscopy. which is
the branch of Optics dealing with spect analysis (. 73,
developed from the research of Newton. Walia Hyde
‘Wollaston (1765-1828) made the erst observations of he
dark ines nthe solar spectram (802). Because ol he sl
Shaped aprtre generally used in specrocopes, the output
conn a core ond El Messe
AS
NE
(0747-1826 ei extended he tjs, Ar achemaly
‘ny sang and made he fr wavelength eventos
{ing din pangs 9.276) Dosis Robert Kiet
Uiticiser and Rote Wilhelm Bunsen C8t1-180)
Serine together at Nee er, stabbed that cach in of
is. Andin 191 ei Henrik aid Boh ARS ID se
specu. Te Em yan som snow understood
bain of modem quantum theory, which desebes the most
nad wi ropero a ben.
The fomi of applied Opus and tal e
aera enges un nights of comicos
ry Jus the er of omer provides ener mesi
ich sulin pecs of mean hecameprospe
Ga Femelle ve serias brad
ae opal phones Bound jeer y ke mabe
matical formalismo! Fourier analysis (302), the outgrowths
saa intrest re the theory of image Tomaten and evalu
tion p $29) te ange encino ($80), and the Wen of
spatial filtering 9.310.
“The aseat ofthe high-speed digita computer brought
systems. Aspherical lens elements (p. 150) took on renewed
practical significance and he dracon limi system with
An pareil el of vien became asl, THe techn
‘fon bombardieat polishing, in which one atom at aimes
‘cision inthe preparation of optical elements, The se of
Single and mulblaye nm coatings (electing. nto
‘volved into a practical communications tool (p. 197). aná
‘hifi gb guides comic be tudes. A pres deal of
tention was ai 1 the infra end of the spectrum (sur
veilance systems, missle gudance te} an this in ter
eganto be ued extensively Opis lens element. replica
graines ben aspen). ne las of paria vi
Be sm comma wth ceeding ow feral eau
as developed, A resurgence the sonsrcion of sono
ing aros the whole spectrum was well der way bythe end
‘he 1960s and vor sun ate OM and 1990
“Te fit ase was ni in 1960, and within a decade ase
avalbli of high power cokarent source let he dow
Cy a number of tow opal efes (harmonic generation,
query mixin te} an thence toa panorama marc,
ac devices. The technology needed 1 produce a practicable
apical comunica stem developed il. The soph:
erator (p64), leeworptic and acoust-opic modulators,
‘rsa opie The saven! remontée own
‘Simesiaal images, ss fue fo hate numerous ation
application este tesis data soe, e.
Work in the 1960s continued in the 1970s, 1980, and he
1990 wth aed vigor, Tat echnolog nest Optics
lies to “death ays” and infared gadget that se in the dark
improve th quai fife have brought producto eds
ine inthe onsumer marketplace as never before, Today
‘ooms. cute Sel in factories Scanning labs in supermar
lea ad performing surgery a hosp. Millions of opal
king al around the word. Tae alms exclusive us. ur
‘rans das now rapid giving sayo mare cient opt
al techniques. À fateaching evolution in the methods f
pet au comte informatian a qi tag
as, a revolution tat wil conse change or ives ne
Profound insights ar slow in coming, What few we have
took over tee howard years to glean even hough lhe pace
bay change while the question muay remains aria
ren Praca wd cM Stas, Gen Speen A
saa intrest re the theory of image Tomaten and evalu
tion p $29) te ange encino ($80), and the Wen of
spatial filtering 9.310.
“The aseat ofthe high-speed digita computer brought
systems. Aspherical lens elements (p. 150) took on renewed
practical significance and he dracon limi system with
An pareil el of vien became asl, THe techn
‘fon bombardieat polishing, in which one atom at aimes
‘cision inthe preparation of optical elements, The se of
Single and mulblaye nm coatings (electing. nto
‘volved into a practical communications tool (p. 197). aná
‘hifi gb guides comic be tudes. A pres deal of
tention was ai 1 the infra end of the spectrum (sur
veilance systems, missle gudance te} an this in ter
eganto be ued extensively Opis lens element. replica
graines ben aspen). ne las of paria vi
Be sm comma wth ceeding ow feral eau
as developed, A resurgence the sonsrcion of sono
ing aros the whole spectrum was well der way bythe end
‘he 1960s and vor sun ate OM and 1990
“Te fit ase was ni in 1960, and within a decade ase
avalbli of high power cokarent source let he dow
Cy a number of tow opal efes (harmonic generation,
query mixin te} an thence toa panorama marc,
ac devices. The technology needed 1 produce a practicable
apical comunica stem developed il. The soph:
erator (p64), leeworptic and acoust-opic modulators,
‘rsa opie The saven! remontée own
‘Simesiaal images, ss fue fo hate numerous ation
application este tesis data soe, e.
Work in the 1960s continued in the 1970s, 1980, and he
1990 wth aed vigor, Tat echnolog nest Optics
lies to “death ays” and infared gadget that se in the dark
improve th quai fife have brought producto eds
ine inthe onsumer marketplace as never before, Today
‘ooms. cute Sel in factories Scanning labs in supermar
lea ad performing surgery a hosp. Millions of opal
king al around the word. Tae alms exclusive us. ur
‘rans das now rapid giving sayo mare cient opt
al techniques. À fateaching evolution in the methods f
pet au comte informatian a qi tag
as, a revolution tat wil conse change or ives ne
Profound insights ar slow in coming, What few we have
took over tee howard years to glean even hough lhe pace
bay change while the question muay remains aria
ren Praca wd cM Stas, Gen Speen A
The sue ofthe actual atte flight cent o complete
semen of Optics, and we will struggle wach roughaut
nomeron ota panicle phenomenon!” sar more complicated
ff parce iss loclizalin; i exis ina well defined
familiar like a ball ora pebble an shrink it dow in imagina-
‘a asthe avis forthe concept of pan Bura Bll
interacts with the Earth (and the Moon, and Sun, et). This
separated rom the bat an imetricable pat ofthe ball just
piles neos va eld and na ere, the eld the par
domain of Quantum Feld Theory. ip wel lk moe
Shoat te (p. 139) Slice ito say now that if ight à
steam of abmicrocopi paces (hats) they ar by o
‘pean ordinary” nial clase! price
"On heiter hand. tie esental feature of wat sino:
arrbance of ames, hich mote wach pace mans
econ But when we lok lovely a gel waves (out an waves
on sino) we se composie phenomena comprised of vast
amber of pacs moving in concert The me sporting
these mates ae atomic (Le parle), ads the waves ae
not continuous nte in an of themselves. Te oly pos
Bi exception night be th elcromagoetic wave. Concept
a consiauous emy and i serves as the model forthe very
: Wave Motion
y we found tha the energy ofan electromagnetic ave iso
tromagnetic theory of light, however wonderll i Ison a
snacroscopi etl is rely eos ici
Tove. Einstein was efit to suggestihat he clectomagne
is wave, which we perceive macroscopically the xt]
maison of fundaneatly geatular underying miro
sleal concept of physical wave Ian ilusion. Sti in the
Tarp scale regime in which we ordinario, eletomag
netic waves seem eal enough and classical theory applies
"cose but the classical andquancun- mechanical ea
rent of igh make se ofthe mathematical description of
raves, thi chapter ay othe bass of what both formal
sms wil need, The ideas we develop her will apply to all
hy waves toma surfs tension ipl ina cup of eto
pul of ight caching us rom some ian galaxy
2.1 One-Dimensional Waves
Anes apesto travel wave tha its a seu
ani disturbance ofthe medium through which eprops
tex, The mos familia waves, andthe ases o vie
msn, surface waves on ui. sound waves In te ai,
compression waves in both solid aná Mid. Sound waves
are longitudinal she medium à placed in the direction of
sion of the wove, Waves ona sting (and electromagnetic
io perprdicular 1 at of the mation of he mare. ln all
semen of Optics, and we will struggle wach roughaut
nomeron ota panicle phenomenon!” sar more complicated
ff parce iss loclizalin; i exis ina well defined
familiar like a ball ora pebble an shrink it dow in imagina-
‘a asthe avis forthe concept of pan Bura Bll
interacts with the Earth (and the Moon, and Sun, et). This
separated rom the bat an imetricable pat ofthe ball just
piles neos va eld and na ere, the eld the par
domain of Quantum Feld Theory. ip wel lk moe
Shoat te (p. 139) Slice ito say now that if ight à
steam of abmicrocopi paces (hats) they ar by o
‘pean ordinary” nial clase! price
"On heiter hand. tie esental feature of wat sino:
arrbance of ames, hich mote wach pace mans
econ But when we lok lovely a gel waves (out an waves
on sino) we se composie phenomena comprised of vast
amber of pacs moving in concert The me sporting
these mates ae atomic (Le parle), ads the waves ae
not continuous nte in an of themselves. Te oly pos
Bi exception night be th elcromagoetic wave. Concept
a consiauous emy and i serves as the model forthe very
: Wave Motion
y we found tha the energy ofan electromagnetic ave iso
tromagnetic theory of light, however wonderll i Ison a
snacroscopi etl is rely eos ici
Tove. Einstein was efit to suggestihat he clectomagne
is wave, which we perceive macroscopically the xt]
maison of fundaneatly geatular underying miro
sleal concept of physical wave Ian ilusion. Sti in the
Tarp scale regime in which we ordinario, eletomag
netic waves seem eal enough and classical theory applies
"cose but the classical andquancun- mechanical ea
rent of igh make se ofthe mathematical description of
raves, thi chapter ay othe bass of what both formal
sms wil need, The ideas we develop her will apply to all
hy waves toma surfs tension ipl ina cup of eto
pul of ight caching us rom some ian galaxy
2.1 One-Dimensional Waves
Anes apesto travel wave tha its a seu
ani disturbance ofthe medium through which eprops
tex, The mos familia waves, andthe ases o vie
msn, surface waves on ui. sound waves In te ai,
compression waves in both solid aná Mid. Sound waves
are longitudinal she medium à placed in the direction of
sion of the wove, Waves ona sting (and electromagnetic
io perprdicular 1 at of the mation of he mare. ln all
‘roo medium; he ind pricpating som rea
i oma steam of
lk only says io
lo recognize that a wave docs not transport the medium.
2 tion with a constant speed The pei alue the
tea dphcenenr ofthe
netic wae (or even the quantum-mechanial probability
rode far Wave
dstrbance e moving, it must hea function of
PTY en
were fs com if function or wave
ape Th which shows apuhe
relie in be stations ste Sa sped
Te shape an instant say =D, cante
BE a RR Ti
represen the prof of the wave tat time. or example
igus 22 Ru on ste
i oma steam of
lk only says io
lo recognize that a wave docs not transport the medium.
2 tion with a constant speed The pei alue the
tea dphcenenr ofthe
netic wae (or even the quantum-mechanial probability
rode far Wave
dstrbance e moving, it must hea function of
PTY en
were fs com if function or wave
ape Th which shows apuhe
relie in be stations ste Sa sped
Te shape an instant say =D, cante
BE a RR Ti
represen the prof of the wave tat time. or example
igus 22 Ru on ste
el asis iva Gasta funtion. (Sarg Mx mas
itsymumsical around the = Dain) Sting t= Oís alo:
9° Farıbe moment we limit ourselves oa wave thal does no
‘change shape progress hough pace, Aer ime +
the pulse hs moved slong the x xi distance, bt in all
‘othr especs remain unakered, We now itroduea coor
ihe speeds In thin system gis no longer a function of me,
aid ar we move alo with S; we sees atonary constant
than ko ha -
von »
“Te distance ook he same at any vale of in Said
‘We now want to rewrite Eq. (2.3 in terms of wget he
‘wave ase would be described by someone at ret So
lows fom ig 23c hat
es
ota = fr = on es
This then presets the mos general orm othe one-dimen
sional wavehuntion. Tobe more specific, we have only o
‘hoo a shape Ea, (22) and then subsite («= of fori
Jin The resulting expresion describes a wave having the
desire profit, moving in he poste direction with a
Speed Thos, Hi. 1 = € "© © ina hellahaped ware
amp for a secc pulse, for example 8)
AIDE + = fx. Mat profiles loin Pi. 2 dm, aif
devas ave on ares would e the sentia dplcement
and we might son replace ty the symbol. Wheher ep
resents placement prets een ld we no are
itsymumsical around the = Dain) Sting t= Oís alo:
9° Farıbe moment we limit ourselves oa wave thal does no
‘change shape progress hough pace, Aer ime +
the pulse hs moved slong the x xi distance, bt in all
‘othr especs remain unakered, We now itroduea coor
ihe speeds In thin system gis no longer a function of me,
aid ar we move alo with S; we sees atonary constant
than ko ha -
von »
“Te distance ook he same at any vale of in Said
‘We now want to rewrite Eq. (2.3 in terms of wget he
‘wave ase would be described by someone at ret So
lows fom ig 23c hat
es
ota = fr = on es
This then presets the mos general orm othe one-dimen
sional wavehuntion. Tobe more specific, we have only o
‘hoo a shape Ea, (22) and then subsite («= of fori
Jin The resulting expresion describes a wave having the
desire profit, moving in he poste direction with a
Speed Thos, Hi. 1 = € "© © ina hellahaped ware
amp for a secc pulse, for example 8)
AIDE + = fx. Mat profiles loin Pi. 2 dm, aif
devas ave on ares would e the sentia dplcement
and we might son replace ty the symbol. Wheher ep
resents placement prets een ld we no are
toa into te description fa wave moving in he positive
edicion aa speed y, we replace x wherever it peas In
Js) by = ter yield u. = DOG = 107 +
AA ably et qua to,say. LD and funtion
ispliiedsucnivelyatr ere 11” 75 are Fee
Fi, 248, which shows te pole sling of tothe right at
subsites Cx + en fr x inthe profile funcion, de resulting.
Te we check the form of E, (25) by examining 0 aran
incre nine of Arand a curesponding increase of 8 Ar
ES
‘Silay the wave was traveling a he negative ice
on that st he I, (25) woul become
Behera wih 030 es
We may sonsudeteefore that parles fu shape of he
A a un, at, single viable the form (v3 3
Equation (2) le erprese equivalent as some fae
“The pute shown in Fig. 22 nd distance described
ty Eq (LS) are spoken of one-dimensional became the
waves sweep over pont ying ona inci takes Day one
tat in his particular case he ope happens to ise up ito a
ages out cross surface, ie the rpples on a pond, and an
2.1.1 The Differential Wave Equation
In 1787 Jean Le Rond lebe insu pati fee
alegatos in the mathematical ween of pyc. Tat
Swings in which the so-called ferential wave equation
res paria diferent equation sas tbn aho defi
ae lot of fern kinds of waves, and each is described by
its own waefineion a). Some are writen nes a pe
Sure. or displacement. while lic deal with lesiromagretc
{eld but emurkaly all ich wavefunctions are sions of
the same diferent wave equation. The reason its pur
real equation i that te wave must De a funcion ot
tie A near itferetal equations semaine cons
ing of oor ore teres ch composé of sets a
plying foncon ta rs deivaies The relevant pois
that each such term must appear nl to the fi poner, nor
an hers be any rose pedi 9 wi derivatives or of
is derivatives Recal hat the onder of dira! ain
qu the orderof te shot deriva in ht equation, Fr
ihernore, ia diferent equation is of ore" Nhe solo
"We now drive the one dimensional form of tHe wave
equation guided by the foreknowledge (7 1) tha he most
basic of waves traveling ata fined speed rues o con
and this suggests second derivatives. cat thee a two
Independent vanables (hr, rand) we can uke he crave
of de with expect to either ors Ths done by ast
Renan wih rsp to one variable an eating th eter
a ai ro conan The san pls or Bee py
But to make the sición evident the panal derivaie be
To late the space and ime dependencies of x) take
she pia estas of x)= wh especial
ing Feonsant, Using == and insmuchas
wor
wee Y
Holding const he pail derivative wth expect im
NAAA x
Gm = 50
edicion aa speed y, we replace x wherever it peas In
Js) by = ter yield u. = DOG = 107 +
AA ably et qua to,say. LD and funtion
ispliiedsucnivelyatr ere 11” 75 are Fee
Fi, 248, which shows te pole sling of tothe right at
subsites Cx + en fr x inthe profile funcion, de resulting.
Te we check the form of E, (25) by examining 0 aran
incre nine of Arand a curesponding increase of 8 Ar
ES
‘Silay the wave was traveling a he negative ice
on that st he I, (25) woul become
Behera wih 030 es
We may sonsudeteefore that parles fu shape of he
A a un, at, single viable the form (v3 3
Equation (2) le erprese equivalent as some fae
“The pute shown in Fig. 22 nd distance described
ty Eq (LS) are spoken of one-dimensional became the
waves sweep over pont ying ona inci takes Day one
tat in his particular case he ope happens to ise up ito a
ages out cross surface, ie the rpples on a pond, and an
2.1.1 The Differential Wave Equation
In 1787 Jean Le Rond lebe insu pati fee
alegatos in the mathematical ween of pyc. Tat
Swings in which the so-called ferential wave equation
res paria diferent equation sas tbn aho defi
ae lot of fern kinds of waves, and each is described by
its own waefineion a). Some are writen nes a pe
Sure. or displacement. while lic deal with lesiromagretc
{eld but emurkaly all ich wavefunctions are sions of
the same diferent wave equation. The reason its pur
real equation i that te wave must De a funcion ot
tie A near itferetal equations semaine cons
ing of oor ore teres ch composé of sets a
plying foncon ta rs deivaies The relevant pois
that each such term must appear nl to the fi poner, nor
an hers be any rose pedi 9 wi derivatives or of
is derivatives Recal hat the onder of dira! ain
qu the orderof te shot deriva in ht equation, Fr
ihernore, ia diferent equation is of ore" Nhe solo
"We now drive the one dimensional form of tHe wave
equation guided by the foreknowledge (7 1) tha he most
basic of waves traveling ata fined speed rues o con
and this suggests second derivatives. cat thee a two
Independent vanables (hr, rand) we can uke he crave
of de with expect to either ors Ths done by ast
Renan wih rsp to one variable an eating th eter
a ai ro conan The san pls or Bee py
But to make the sición evident the panal derivaie be
To late the space and ime dependencies of x) take
she pia estas of x)= wh especial
ing Feonsant, Using == and insmuchas
wor
wee Y
Holding const he pail derivative wth expect im
NAAA x
Gm = 50
Combining Bas 8) and Sis
This say that he rate of ange of wih sand with are
cei iti amullcatve comen sd in ig 25.
The second pra derivatives of Eqs (28) and (29) re
len
le)
Coming this wit Bg 10 we bin
Y ee =
wor
don Ina equation fr undamped tens hat So
lc of damping canbe Severed by aiding ina arte
theo yelen variation of 4.2.1 1-an fom tha he com
SC te leere wave res ina completly an
Alan
waves ana a rc profi. Sl Ut simpl tmp
tion as ld at the geral formulation, te diferent ane
‘uation I fanetion that epesentsa wave à sion of
2.2 Harmonic Waves
Let ow examin simples wave frm, one for which he
Chooses the poe he simple Fac —
Hy =H) = Ain B= fin E
This say that he rate of ange of wih sand with are
cei iti amullcatve comen sd in ig 25.
The second pra derivatives of Eqs (28) and (29) re
len
le)
Coming this wit Bg 10 we bin
Y ee =
wor
don Ina equation fr undamped tens hat So
lc of damping canbe Severed by aiding ina arte
theo yelen variation of 4.2.1 1-an fom tha he com
SC te leere wave res ina completly an
Alan
waves ana a rc profi. Sl Ut simpl tmp
tion as ld at the geral formulation, te diferent ane
‘uation I fanetion that epesentsa wave à sion of
2.2 Harmonic Waves
Let ow examin simples wave frm, one for which he
Chooses the poe he simple Fac —
Hy =H) = Ain B= fin E
where is a postive constant known as he propagation
number. I's necesay o inrodece the coast À spy
nis The ine the aio two lengths andi therefore un
les Accordingly. pope nadia, which iota eal
physical wit Te sine vars rom +140 a ae ma
imma Yel is A Thi ak ance sn
the amplitude ofthe wave (Fig. 2.6), To transform Eg
itive direction, we need merely replace x by (x = u. in
Pa en
Tie iceteaty sotuion of he ferential wave eun ee
Problem 2.18. Holding cier xo neg results in sn
‘ine, The spatial period ie known st wavelength and is
‘enced by A. Wavelength the amber of ens of length per
tne. The cosomary mesure of isthe nanomete, whee |
fm = 10 ° m alhoygh he miro (1 um = 10 "soften
{ied and he older angstrom (A = 101 m) can sl! be
mount shoul eave Y uted thats ©
WU WA en}
Inthe case ofa harmonie wave this is equivalent o aleros
the pue of he sine fonction by 2. Therefore,
sin ke A) en = sin
sinker) mem
Lean
ms of À. Here y she argument of he sine uncin, als
calé the phase Notice at de) = O whenever in = 0
hich happens when ¢ = Du 20, dr. and soon. Tha oct
Me 0 2.4, and 82; repectiney
In an analogous fashion tothe above discussion ol, we
sow examine the temporal period, This is the amount of
Time Stakes for one compete wave Lo pats à salary
intime hat is of nee, coat “
sin Ge 0 = sin fer ==
The period is the number of nits of tine per wave Fi. 2,
inver of inch is he temporal Frequency». or her
her of eaves pr ani fine ve Fes) Tr,
number. I's necesay o inrodece the coast À spy
nis The ine the aio two lengths andi therefore un
les Accordingly. pope nadia, which iota eal
physical wit Te sine vars rom +140 a ae ma
imma Yel is A Thi ak ance sn
the amplitude ofthe wave (Fig. 2.6), To transform Eg
itive direction, we need merely replace x by (x = u. in
Pa en
Tie iceteaty sotuion of he ferential wave eun ee
Problem 2.18. Holding cier xo neg results in sn
‘ine, The spatial period ie known st wavelength and is
‘enced by A. Wavelength the amber of ens of length per
tne. The cosomary mesure of isthe nanomete, whee |
fm = 10 ° m alhoygh he miro (1 um = 10 "soften
{ied and he older angstrom (A = 101 m) can sl! be
mount shoul eave Y uted thats ©
WU WA en}
Inthe case ofa harmonie wave this is equivalent o aleros
the pue of he sine fonction by 2. Therefore,
sin ke A) en = sin
sinker) mem
Lean
ms of À. Here y she argument of he sine uncin, als
calé the phase Notice at de) = O whenever in = 0
hich happens when ¢ = Du 20, dr. and soon. Tha oct
Me 0 2.4, and 82; repectiney
In an analogous fashion tothe above discussion ol, we
sow examine the temporal period, This is the amount of
Time Stakes for one compete wave Lo pats à salary
intime hat is of nee, coat “
sin Ge 0 = sin fer ==
The period is the number of nits of tine per wave Fi. 2,
inver of inch is he temporal Frequency». or her
her of eaves pr ani fine ve Fes) Tr,
ber quant tote used te rare wave
Deis the angular temporal frequency
given in its of radins per second. The other, whi
«sa e
Deis the angular temporal frequency
given in its of radins per second. The other, whi
«sa e
re 28 u ee sas 8 per re
Fo The Snes om he nave ena ob De
EE
ave as a single constant requency andi hereore mano
Real waves are
«bromatlc o, even betr, monoenerge
never monochromatic. Even a perfect sinusoidal generate
‘cannot have Dec operating forever Is output vil avoid
Pere 23 ras mme at x
wil e encountered most e
stent Thats for any fr valu of, cr so matbemat
ably cota a ange of tequencós albeit small ne just
Tecate the Wate does ot extend Back OF = =, TANT
mo ie wave sg o he quacinonachromate
Before we move one's patsome numer ny 0.13
‘ase how to des with each ter, To tha end, abri et
= 10m and à = 20m Then he wavefunction
= Asin =a
in Sunt taco
dani"
Figure 23 shows how tb wave progresses tthe right at 1.0
sm sasthe tine ges fom! = O [whereupon = Asin e]
P= 10. Inkereupon Y= Asin wer LD = 20
(aleron y= Asin xs 20)
2.3 Phase and Phase Velocity
“The entire argument ofthe sine isthe phase of the wave,
ee a me
= Asin (teat 228)
where eis thei
ll phase. To ge sens of the physical
‘meaning f £ magi hit we wie o pode a progresive
amonio wave ona sche sting. an ig 210 In order
‘0 generate harmonic waves, the and bing th sing woud
ave to move ih that ie serial islasement ya propor
tinal tothe negative ofits acceleration ta, spi ar
‘monic motion (ce Problem 221), Bat at = Oandx = 0, the
‘sud, sin Fig 210. econ. ofcourse, begins motion on
Fo The Snes om he nave ena ob De
EE
ave as a single constant requency andi hereore mano
Real waves are
«bromatlc o, even betr, monoenerge
never monochromatic. Even a perfect sinusoidal generate
‘cannot have Dec operating forever Is output vil avoid
Pere 23 ras mme at x
wil e encountered most e
stent Thats for any fr valu of, cr so matbemat
ably cota a ange of tequencós albeit small ne just
Tecate the Wate does ot extend Back OF = =, TANT
mo ie wave sg o he quacinonachromate
Before we move one's patsome numer ny 0.13
‘ase how to des with each ter, To tha end, abri et
= 10m and à = 20m Then he wavefunction
= Asin =a
in Sunt taco
dani"
Figure 23 shows how tb wave progresses tthe right at 1.0
sm sasthe tine ges fom! = O [whereupon = Asin e]
P= 10. Inkereupon Y= Asin wer LD = 20
(aleron y= Asin xs 20)
2.3 Phase and Phase Velocity
“The entire argument ofthe sine isthe phase of the wave,
ee a me
= Asin (teat 228)
where eis thei
ll phase. To ge sens of the physical
‘meaning f £ magi hit we wie o pode a progresive
amonio wave ona sche sting. an ig 210 In order
‘0 generate harmonic waves, the and bing th sing woud
ave to move ih that ie serial islasement ya propor
tinal tothe negative ofits acceleration ta, spi ar
‘monic motion (ce Problem 221), Bat at = Oandx = 0, the
‘sud, sin Fig 210. econ. ofcourse, begins motion on
28. Capo 2 vn son
mathematical more apeaing an another the etre
ith Both and mew et
‘hang of phase nih tne oF
[joey
Er
I
Pain of the wave, ene at which pin onthe pe
a em
Fre 210 vere orto ae
squat ==
“ duos 3
Spee orton long me, the a a
menta mg (2
‘oflen the case, whom he initial phase so no paricularsigil- Aste 2 A
mathematical more apeaing an another the etre
ith Both and mew et
‘hang of phase nih tne oF
[joey
Er
I
Pain of the wave, ene at which pin onthe pe
a em
Fre 210 vere orto ae
squat ==
“ duos 3
Spee orton long me, the a a
menta mg (2
‘oflen the case, whom he initial phase so no paricularsigil- Aste 2 A
through he same number of cycles per second a the wave.
Foreach yee 6 changes by 20,
Similar, the eof change of phase
im distance hol
(2 em
These two expressions should bin to mind an equation
from te theory of peal derivatives oe sed frequent ln
Termodynamies, amy
The em onthe ll represents be speed of propagation ofthe
condition af consent phase Imagine Banmonte wave and
‘hoote any plat onthe Profile. or example, a rest ofthe
Save. Asthe wave moves troup space, the displacement y
i the rest remis fixed, Since the only variable inthe bar
‘monic wavefunction is the phase, to must Be costa for
that moving pin. That, the phase is fined at sucha vale as
to eld he constant y oresponding tthe chosen pont. The
pet moves lone with he profile at he sped, and 0 00
Taking the appropriate paral derivatives of as given, for
example. by a. (2.29) and substan them nto Ex. (2.32)
(2) -=2-> es
“Thisisthe sped at wich th profile moves andi Know com
‘monly asthe phase ely ote wave. The phase veocy is
accompanied by a poive sign when the wave moves in he
ran finca x anda negative oe in he direcion of
decreasing x This conste with our development of as.
Consider the idea ofthe propagation of constant phase
aná how it elles o any one ofthe harmonic wave equ
B= Anz
with 2 Kao = constant
As inceaen, must incense. Even ix < Oso tha @< x
mustineease (Le, esom ls egaive), Her, thn, the on
dition of cont phase moves in the direcion o increasing
As ong a he to terms in he pe subir from euch th
the wae travel te pose eircio, On the other
Ind for
2 = Me + 09 = constant
as increases can be positive and decreasing or negative and
Becoming more negative. nether case, he const pate
Any point on a harmonie wave having a fixed marido
det) =O, or alleraively, dia 1/4 = 0. This ve
forall waves, periodic or ot and tead Problem 227) 0
theexpession|
09/30, =
= pan, Ze
which an be used to conveniently provide wen we have
Ses Nea ca nang aie er at
negative «rein
Figure 212 depicts a source producing hypotbeticl ro
mensional waves onthe surface of abi. Te esenialy
Hals vides In be cagam But theres anote seta way
6 vision what's happening, The curves conecto el he
Shot.
ye
Fee 212 Ceci es ao
Foreach yee 6 changes by 20,
Similar, the eof change of phase
im distance hol
(2 em
These two expressions should bin to mind an equation
from te theory of peal derivatives oe sed frequent ln
Termodynamies, amy
The em onthe ll represents be speed of propagation ofthe
condition af consent phase Imagine Banmonte wave and
‘hoote any plat onthe Profile. or example, a rest ofthe
Save. Asthe wave moves troup space, the displacement y
i the rest remis fixed, Since the only variable inthe bar
‘monic wavefunction is the phase, to must Be costa for
that moving pin. That, the phase is fined at sucha vale as
to eld he constant y oresponding tthe chosen pont. The
pet moves lone with he profile at he sped, and 0 00
Taking the appropriate paral derivatives of as given, for
example. by a. (2.29) and substan them nto Ex. (2.32)
(2) -=2-> es
“Thisisthe sped at wich th profile moves andi Know com
‘monly asthe phase ely ote wave. The phase veocy is
accompanied by a poive sign when the wave moves in he
ran finca x anda negative oe in he direcion of
decreasing x This conste with our development of as.
Consider the idea ofthe propagation of constant phase
aná how it elles o any one ofthe harmonic wave equ
B= Anz
with 2 Kao = constant
As inceaen, must incense. Even ix < Oso tha @< x
mustineease (Le, esom ls egaive), Her, thn, the on
dition of cont phase moves in the direcion o increasing
As ong a he to terms in he pe subir from euch th
the wae travel te pose eircio, On the other
Ind for
2 = Me + 09 = constant
as increases can be positive and decreasing or negative and
Becoming more negative. nether case, he const pate
Any point on a harmonie wave having a fixed marido
det) =O, or alleraively, dia 1/4 = 0. This ve
forall waves, periodic or ot and tead Problem 227) 0
theexpession|
09/30, =
= pan, Ze
which an be used to conveniently provide wen we have
Ses Nea ca nang aie er at
negative «rein
Figure 212 depicts a source producing hypotbeticl ro
mensional waves onthe surface of abi. Te esenialy
Hals vides In be cagam But theres anote seta way
6 vision what's happening, The curves conecto el he
Shot.
ye
Fee 212 Ceci es ao
pins witha given phase form set concentre lle. Pa
thermore, ven that Ais everywhere constant at anyone ds
nee fom tic om. can ver ci Sa ms
Be constant over that cel. In aer word ll he core
sponding peak and troughs al on cies and we speak of
peo
2.4 The Superposition Principle
The fof de dierent wave equation [OLD] reveal
an niguing ropeny of wave, ore ha quite nike the
ein o team of classical parce. Suppose ht the
snaefuncions à, and d ae each separate slain ofthe
‘nave equ flow that (+ 9s) lo a oo,
This know she Superposition Principle, and cane.
inspace wherein they overlap they wil simply dto (oF sub
pú ether wave The eran disturbance at each point
Inthe region of verlp isthe algebra sum ofthe individual
onsen! waves at that locaton Fg, 213, Once having
assed rapie eon where the to waves EG a
Sill move eat and ay wall by the counter
‘Keep in mind tat we are an abo a Hear supers
‘monly encountered. Nonetheless also possible forthe
‘wave amplitudes oe age enh to dive fhe medium ina
Aoninear fashion (639, Forte une being we" concen
trate on teins ferential wave equation, wich res m
Mach of Opts maires he sopepoion of waves in
relation are manietations of ie satin flight from
Pi 212 De pa ts cba nih
ail aa (8x PER a a OB
‘sisson in ems of he overagping of waves ethene
comes cca ba we undenand the proces ates qu
sale o) we simply add and 9, eher of which could be
sive reganve Aca qc esc, Kee mi tater
erde seals the vale of the or nonzero conse
ave = Sand thee uo cures roe a tat octo y
stds = and + 314 ra OF te oer ans, 0 wherever
thet came ses fav el is and ep
‘pts (eg. tha ~ +267 rah nde. nic bow are
Ani 0 he ef ith pesto by Ora
Developing the ilusiona bt further Fig, 216 shows
ow the resulta aii from th supers of wo ely
Span pito waves pend nthe pros ane deren
ete them: In Fig. 2.14 te two corset! waves have
the same phase; hai her phase angl diference ls er,
‘enforcing eachother, The composite wave which then a
thermore, ven that Ais everywhere constant at anyone ds
nee fom tic om. can ver ci Sa ms
Be constant over that cel. In aer word ll he core
sponding peak and troughs al on cies and we speak of
peo
2.4 The Superposition Principle
The fof de dierent wave equation [OLD] reveal
an niguing ropeny of wave, ore ha quite nike the
ein o team of classical parce. Suppose ht the
snaefuncions à, and d ae each separate slain ofthe
‘nave equ flow that (+ 9s) lo a oo,
This know she Superposition Principle, and cane.
inspace wherein they overlap they wil simply dto (oF sub
pú ether wave The eran disturbance at each point
Inthe region of verlp isthe algebra sum ofthe individual
onsen! waves at that locaton Fg, 213, Once having
assed rapie eon where the to waves EG a
Sill move eat and ay wall by the counter
‘Keep in mind tat we are an abo a Hear supers
‘monly encountered. Nonetheless also possible forthe
‘wave amplitudes oe age enh to dive fhe medium ina
Aoninear fashion (639, Forte une being we" concen
trate on teins ferential wave equation, wich res m
Mach of Opts maires he sopepoion of waves in
relation are manietations of ie satin flight from
Pi 212 De pa ts cba nih
ail aa (8x PER a a OB
‘sisson in ems of he overagping of waves ethene
comes cca ba we undenand the proces ates qu
sale o) we simply add and 9, eher of which could be
sive reganve Aca qc esc, Kee mi tater
erde seals the vale of the or nonzero conse
ave = Sand thee uo cures roe a tat octo y
stds = and + 314 ra OF te oer ans, 0 wherever
thet came ses fav el is and ep
‘pts (eg. tha ~ +267 rah nde. nic bow are
Ani 0 he ef ith pesto by Ora
Developing the ilusiona bt further Fig, 216 shows
ow the resulta aii from th supers of wo ely
Span pito waves pend nthe pros ane deren
ete them: In Fig. 2.14 te two corset! waves have
the same phase; hai her phase angl diference ls er,
‘enforcing eachother, The composite wave which then a
the sequence ofthe drawings, we se ale saltan amp
tase diminishes as e pase ange ference incrsses il
ing. 2 1d, almost vanishes when ar ference eu
The vasos re hen sai to be 10° outt phase The at hat
waves mich ar otha tend 1 diminih each eter has
Bien th rame interference o he sole phenomenon
2.5 The Complex Representation
As we develop the analysis of wave phenomena it will
Become evident ar he sine ad cosine functions that desc
harmonic waves can be someuhat aukwan or our purposes
The expressions formulated wil sometimes ber involved
andthe trigonometric manipulations required to cope with
‘hem willbe even more native. The complex-number
rally simpler fo process. fc, complex exponential are
‘red encino Casa ac Quantum Mecanica a
“Te complex number has he form
CT ta sc
a) ard 2 ach yo rat
tively randy, where bat and are themesves rea num
Fig. 2.1Se. ln terms of polar coordinates (. 8,
zur y=rsind
ond a+ = rer 8+ isin 8
The Est formaté
moros ind
leads tothe expression 4 = cos - sin @ and dig and
baci these two equations sets
tase diminishes as e pase ange ference incrsses il
ing. 2 1d, almost vanishes when ar ference eu
The vasos re hen sai to be 10° outt phase The at hat
waves mich ar otha tend 1 diminih each eter has
Bien th rame interference o he sole phenomenon
2.5 The Complex Representation
As we develop the analysis of wave phenomena it will
Become evident ar he sine ad cosine functions that desc
harmonic waves can be someuhat aukwan or our purposes
The expressions formulated wil sometimes ber involved
andthe trigonometric manipulations required to cope with
‘hem willbe even more native. The complex-number
rally simpler fo process. fc, complex exponential are
‘red encino Casa ac Quantum Mecanica a
“Te complex number has he form
CT ta sc
a) ard 2 ach yo rat
tively randy, where bat and are themesves rea num
Fig. 2.1Se. ln terms of polar coordinates (. 8,
zur y=rsind
ond a+ = rer 8+ isin 8
The Est formaté
moros ind
leads tothe expression 4 = cos - sin @ and dig and
baci these two equations sets
22 Caper 2 ter
sige hry il Moco wen eco,
on sinó
raie The magnitud is ofen denoted El and refered
the modular o brote ne of ae complex number. The
complex confugate,Indiato by an seri Pi. 2150).
found by epica (wherever appear, with 50 that
The operations of addition and subucion ae quite sight
PEPE ET
Notice a this process is very much ik the component dde
and =
Amber facts tht wil be wel in fur acuse
‘ell worth mentioning a bis po. I Tollows rom te er
nary tigonometi addition formulas (Problem 2.37) that
ani = and à = iy
rer
Simian
The union ei period hat i repeats el every
Any complex number can Be represents We Su
real part Re (3) and imaginary par
veh that
ReG = IE +9 and
Ah 0 these expressions: follow immediately from e
sige hry il Moco wen eco,
on sinó
raie The magnitud is ofen denoted El and refered
the modular o brote ne of ae complex number. The
complex confugate,Indiato by an seri Pi. 2150).
found by epica (wherever appear, with 50 that
The operations of addition and subucion ae quite sight
PEPE ET
Notice a this process is very much ik the component dde
and =
Amber facts tht wil be wel in fur acuse
‘ell worth mentioning a bis po. I Tollows rom te er
nary tigonometi addition formulas (Problem 2.37) that
ani = and à = iy
rer
Simian
The union ei period hat i repeats el every
Any complex number can Be represents We Su
real part Re (3) and imaginary par
veh that
ReG = IE +9 and
Ah 0 these expressions: follow immediately from e
Argan diagram, Fig 2.10 and. For example, 2 + 2°
because the Imspiary pars cancel, amé so Re (2) © x
From he pla fom where
ROTAR ROTO
it is clear tit either part sold he chosen to describe a ar
mont wave. ie uma, however to choose te espa,
in bic case a harmonic waved nen at
Hs. = Read es
ich is cos, evant to
This is done to take advantage of theese wi which complex
expesenials can be musiputed Only alr avis at a al
rs wetake he ral ars, coria y become quie
common to rte $x as EQ. 37) where is under
ood thatthe at ways the cl pr.
2.6 Phasors and the Addition
of Waves
‘The aow in he Argand diagram (ig 2.54) is set rowing
Frequency by eig the angle equal of Tis suggests
à scheme Tor represenin (and alimely nine) waves
"tat we will introduce here quatre} and develop aer
‘of amplitude A tavein the lef. The arrow ithe diagram
sharing angle makes wth he reference ad io Tis
{ute a phasor. which tells us everything we need to know
tout Ihe conesponding harmonic wave. I+ common lo
express phasar in tems is amplude ant pase a
Tose ow tis works, le’ fist examine each par of Fig
2.16separely. The por in Fi. 26a hs a ero phase
along the reference ai
angle that sored
Phasar as phase angle of + ad, andthe sine carve is
sak a smaller salu ak an docs he reerence curve
Para) and therefore it ead the reference by rad I
Dts), ad o) of Fig 216, he phase angles are 4/2
fad, "29/3 rad, and <r rad, repose. The entre
FEU of rvs a be ee aE 4 2 A HG
traveling 1 the eft Weis equivalen represented by a
or scan eounterelockwie such tha it phase ange at
ÉRIC und
because the Imspiary pars cancel, amé so Re (2) © x
From he pla fom where
ROTAR ROTO
it is clear tit either part sold he chosen to describe a ar
mont wave. ie uma, however to choose te espa,
in bic case a harmonic waved nen at
Hs. = Read es
ich is cos, evant to
This is done to take advantage of theese wi which complex
expesenials can be musiputed Only alr avis at a al
rs wetake he ral ars, coria y become quie
common to rte $x as EQ. 37) where is under
ood thatthe at ways the cl pr.
2.6 Phasors and the Addition
of Waves
‘The aow in he Argand diagram (ig 2.54) is set rowing
Frequency by eig the angle equal of Tis suggests
à scheme Tor represenin (and alimely nine) waves
"tat we will introduce here quatre} and develop aer
‘of amplitude A tavein the lef. The arrow ithe diagram
sharing angle makes wth he reference ad io Tis
{ute a phasor. which tells us everything we need to know
tout Ihe conesponding harmonic wave. I+ common lo
express phasar in tems is amplude ant pase a
Tose ow tis works, le’ fist examine each par of Fig
2.16separely. The por in Fi. 26a hs a ero phase
along the reference ai
angle that sored
Phasar as phase angle of + ad, andthe sine carve is
sak a smaller salu ak an docs he reerence curve
Para) and therefore it ead the reference by rad I
Dts), ad o) of Fig 216, he phase angles are 4/2
fad, "29/3 rad, and <r rad, repose. The entre
FEU of rvs a be ee aE 4 2 A HG
traveling 1 the eft Weis equivalen represented by a
or scan eounterelockwie such tha it phase ange at
ÉRIC und
ang amples oF, = 10,
Mba, 09 ad ses de
butter the wave advances to th ight ande has lates
ie
ested inthe reslig amplitude and phase. Wi ea in mind
reexamine te way aves add together in Fig. 2.14. Apparent
1y. for disturbances that ae pase (Fig, 2. a) the mph
ide of the resultat wave, A, I the sum of he consent
amplitudes À = A; + Ay = 10 +09 = 19. This he same
inte same direcion Sinalarly Fi. 2.144), when the com
ponent waves re IK outof phase À = A; = As = 10-09
aed. At phasor are not eco they do din sim
ir way Later, we'll prove tat vo arity phasors, 2
to produce a resultant AZy. Because both phasors rotate
= Fre 218 Ts oon oh
Loge at arate, we an simply freee them at = and ot
‘worry about crime dependence which makes them lot
“The four phasor diagrams in Fig. 2.1 comespond tothe
{our wave combinaons aking place sequently Fi. 2.4.
‘When the waves are in-phase (asin Fi. 2.130), we tke the
phases ofboth wa] and ave 21 be er (Ff. 2.180) and
postion the emesponding has po alone ern
Feleenc ais, When the waves fern phase by m 3 (asin
Fig, 2 130) the pasos have à relative phase (ig 2.18) of
173. Theresluat, which as an appropiate reduced amp
tude, hea phase gta is between and as an be seen
in bol Figs 2146 nd 2,18, When the two waves iferin
Phase by 2/3 (a in Fig 21), the coresponding phasors
Amos form an equilateral angle is Fig. 218e ut forthe
faetthat > Aa and 5 pow Hes een A and As Ent
ly wheat phase-angle ference forthe nwa waves (and the
eo phasors) is ad... 1807, they alma cancel andthe
reeling ampliado isa minimum. Notice in Fig 2 8) that
the resultant paso poits log the reference ai ando has
{he same phase (16.2000) 6 Ang The Ls 80" auto
phase wil Aa Zen same hing ne be corresponding
Saves in Fig 2.144.
2.7 Plane Waves
‘The plane wave is perp the simples example of «thee
dimensional wave. et at a given ine, when al thes
ace on wich a urbane has constant phase frm a of
ion. There are quite practical reasons for staying hiso of.
ituhance, one of which ta by Using opis eves, we
san ea procure green plate waves:
The matematica expression fo a plane Ua is perpen
ar 10 given vector Rand tht pases though some pint
mb aer say to derive (Fig. 219) Fit we wre
‘he poston vector in Cartesian coordiatsin terms o the unt
ta estos (Fig 2190)
Poio
IR begin a some arbitrary orp 0 and ends a the port
(Gays hich ea, forthe moment be any wherein space.
Sima,
solo yi + ink
Mba, 09 ad ses de
butter the wave advances to th ight ande has lates
ie
ested inthe reslig amplitude and phase. Wi ea in mind
reexamine te way aves add together in Fig. 2.14. Apparent
1y. for disturbances that ae pase (Fig, 2. a) the mph
ide of the resultat wave, A, I the sum of he consent
amplitudes À = A; + Ay = 10 +09 = 19. This he same
inte same direcion Sinalarly Fi. 2.144), when the com
ponent waves re IK outof phase À = A; = As = 10-09
aed. At phasor are not eco they do din sim
ir way Later, we'll prove tat vo arity phasors, 2
to produce a resultant AZy. Because both phasors rotate
= Fre 218 Ts oon oh
Loge at arate, we an simply freee them at = and ot
‘worry about crime dependence which makes them lot
“The four phasor diagrams in Fig. 2.1 comespond tothe
{our wave combinaons aking place sequently Fi. 2.4.
‘When the waves are in-phase (asin Fi. 2.130), we tke the
phases ofboth wa] and ave 21 be er (Ff. 2.180) and
postion the emesponding has po alone ern
Feleenc ais, When the waves fern phase by m 3 (asin
Fig, 2 130) the pasos have à relative phase (ig 2.18) of
173. Theresluat, which as an appropiate reduced amp
tude, hea phase gta is between and as an be seen
in bol Figs 2146 nd 2,18, When the two waves iferin
Phase by 2/3 (a in Fig 21), the coresponding phasors
Amos form an equilateral angle is Fig. 218e ut forthe
faetthat > Aa and 5 pow Hes een A and As Ent
ly wheat phase-angle ference forthe nwa waves (and the
eo phasors) is ad... 1807, they alma cancel andthe
reeling ampliado isa minimum. Notice in Fig 2 8) that
the resultant paso poits log the reference ai ando has
{he same phase (16.2000) 6 Ang The Ls 80" auto
phase wil Aa Zen same hing ne be corresponding
Saves in Fig 2.144.
2.7 Plane Waves
‘The plane wave is perp the simples example of «thee
dimensional wave. et at a given ine, when al thes
ace on wich a urbane has constant phase frm a of
ion. There are quite practical reasons for staying hiso of.
ituhance, one of which ta by Using opis eves, we
san ea procure green plate waves:
The matematica expression fo a plane Ua is perpen
ar 10 given vector Rand tht pases though some pint
mb aer say to derive (Fig. 219) Fit we wre
‘he poston vector in Cartesian coordiatsin terms o the unt
ta estos (Fig 2190)
Poio
IR begin a some arbitrary orp 0 and ends a the port
(Gays hich ea, forthe moment be any wherein space.
Sima,
solo yi + ink
(tesa toe chr
By ing
swe forge the vector — Foto sweep out plane pependcu
Rai ajenk am
uation (238 canbe expressed inthe form.
be = nay bly IAEA AO
wa kathy these em
a kay yg + y= const 0)
"The most cris for of de equation of plane perpen
RE = cons = à ea
have the same projection ono the E directos
namen em
wn=amden s
° rm ack as
plane defined by KF constant Since we are csi
tonic tuts; ney should repeat ten
a aber hole representation of his kind o
have dran only afew of the inci mbr les cs
draws with an init spatial een, since co nits wee put
fon. The dsturtance lal occupies a ol space
Ir LL
The spatial epetive nature of thet harmonic una
BE afer A) m
‘where kis the magna of and R/ki 2 unit estar panel.
og: 2.21. Inthe exponenbal form. this equivale 10
By ing
swe forge the vector — Foto sweep out plane pependcu
Rai ajenk am
uation (238 canbe expressed inthe form.
be = nay bly IAEA AO
wa kathy these em
a kay yg + y= const 0)
"The most cris for of de equation of plane perpen
RE = cons = à ea
have the same projection ono the E directos
namen em
wn=amden s
° rm ack as
plane defined by KF constant Since we are csi
tonic tuts; ney should repeat ten
a aber hole representation of his kind o
have dran only afew of the inci mbr les cs
draws with an init spatial een, since co nits wee put
fon. The dsturtance lal occupies a ol space
Ir LL
The spatial epetive nature of thet harmonic una
BE afer A) m
‘where kis the magna of and R/ki 2 unit estar panel.
og: 2.21. Inthe exponenbal form. this equivale 10
Fare 221 Pare nes.
Forthis tobe tae, we mu have
Teretor
The vector whose magninde i the propagation number k
(already incor). le called the propagation vector.
Aa ed prt in space where Pi comia, pase
constant asis UP in ho, the planes are moines To get
thes moving) mus be made o sy ne some
os aol DY nradheing the lee dependence a
analogous Faso to that of the one dimensional wave, Here
Wit A. nd constant AS this disnbance traves longi
the Keveton we ean assign pise romesponing to Hat
‘ach pint in space and ime. At any given ine the surfaces
Joining al points of equal phase are known as wavefronts,
Note that he wavefunction vil have a consu alcove e
saveron only if the ample À has axed value a every
pont on the waseron In gener A 1a funtion of Fand
may no! De constant overall space o even over a weft
il ot be concerned with this sor of disturbance un ae,
hen we consider imerheam and toa neral reflection
The phase velocity ofa lane wave piven by Pa, 2a)
equivalen to the propagation veloiy of the waverant In
Fig. 221, the sear component o Fin he direction of is
The ia on wavelront x constan so hater ae
‘ifthe oat maves along Ka distance dr, sve must ave
IRALA
Tn enone or, ie
240 es
‘We could have anticipated this eu by rotating the coos:
onen
since RE = A = kr The wave has thereby been fleisch
reduced to Me one-dimensional disturbance already sie
Non consider the twa waves in Fig. 220, oth have the
same wavelength such iat, = Ks == 2/2. Wave
proparalg long me ais an de wie as
igre 222 tno og wos le are woven eg
Forthis tobe tae, we mu have
Teretor
The vector whose magninde i the propagation number k
(already incor). le called the propagation vector.
Aa ed prt in space where Pi comia, pase
constant asis UP in ho, the planes are moines To get
thes moving) mus be made o sy ne some
os aol DY nradheing the lee dependence a
analogous Faso to that of the one dimensional wave, Here
Wit A. nd constant AS this disnbance traves longi
the Keveton we ean assign pise romesponing to Hat
‘ach pint in space and ime. At any given ine the surfaces
Joining al points of equal phase are known as wavefronts,
Note that he wavefunction vil have a consu alcove e
saveron only if the ample À has axed value a every
pont on the waseron In gener A 1a funtion of Fand
may no! De constant overall space o even over a weft
il ot be concerned with this sor of disturbance un ae,
hen we consider imerheam and toa neral reflection
The phase velocity ofa lane wave piven by Pa, 2a)
equivalen to the propagation veloiy of the waverant In
Fig. 221, the sear component o Fin he direction of is
The ia on wavelront x constan so hater ae
‘ifthe oat maves along Ka distance dr, sve must ave
IRALA
Tn enone or, ie
240 es
‘We could have anticipated this eu by rotating the coos:
onen
since RE = A = kr The wave has thereby been fleisch
reduced to Me one-dimensional disturbance already sie
Non consider the twa waves in Fig. 220, oth have the
same wavelength such iat, = Ks == 2/2. Wave
proparalg long me ais an de wie as
igre 222 tno og wos le are woven eg
O ET
region of overlap when we conser interference In more
‘The plane harmonic wave i often writen in-Canesan
‘coors
where. and y sete direction cosines o E se Problem
239) nterms at components, the rapide of he prepa
ton estore
sof sonne
"Wear examined plane wavs witha parcularemphtss
on armonie funcion, The special significance of uote
waves wofol: first, physically, sinusoidal waves canbe
enerte relatively simply y using some form of harmonie
‘uilaor second. any thre-dimencional ware can be
expressed as a combination of plane waves. ach AVI à
Wecan sena imagines series ane waves ike hose
in Fig. 220 here the distance varies in some fashion oh
‘than hormonal (se photo). will be sen in the next
‘of more general la wave solo.
2.8 The Three-Dimensional
Differential Wave Equation
(Oh hee-snensionl naes onl the plane wave thse
‘monie oe na) can move Cough space Wi an unchanging
Profile Cleary teen a wave as a disturbance whose pro
define a wave as any solution of the iernil wave equ
tion: What we need now isa hre-menvonal wave equ.
form by generalizing from te one-dimensional expression,
Eg, (2.11. In Caren coordinates, the poston variable x
and + must certainly appear symmetrically” in Ihe thee
dimensional equation a fatto be Kept in mind, The wave
faction bi sx even by Bq, 2:52) sa puricula sollen.
‘ofthe dferetl equation me are looking for. Inansogy wit
the denivation of Eq (2.1), we comput following paral
Aang the re spatial derivatives and ling the at ar
inte mios coa ley ae fe ae n
Gets ende ee Decor to cage
region of overlap when we conser interference In more
‘The plane harmonic wave i often writen in-Canesan
‘coors
where. and y sete direction cosines o E se Problem
239) nterms at components, the rapide of he prepa
ton estore
sof sonne
"Wear examined plane wavs witha parcularemphtss
on armonie funcion, The special significance of uote
waves wofol: first, physically, sinusoidal waves canbe
enerte relatively simply y using some form of harmonie
‘uilaor second. any thre-dimencional ware can be
expressed as a combination of plane waves. ach AVI à
Wecan sena imagines series ane waves ike hose
in Fig. 220 here the distance varies in some fashion oh
‘than hormonal (se photo). will be sen in the next
‘of more general la wave solo.
2.8 The Three-Dimensional
Differential Wave Equation
(Oh hee-snensionl naes onl the plane wave thse
‘monie oe na) can move Cough space Wi an unchanging
Profile Cleary teen a wave as a disturbance whose pro
define a wave as any solution of the iernil wave equ
tion: What we need now isa hre-menvonal wave equ.
form by generalizing from te one-dimensional expression,
Eg, (2.11. In Caren coordinates, the poston variable x
and + must certainly appear symmetrically” in Ihe thee
dimensional equation a fatto be Kept in mind, The wave
faction bi sx even by Bq, 2:52) sa puricula sollen.
‘ofthe dferetl equation me are looking for. Inansogy wit
the denivation of Eq (2.1), we comput following paral
Aang the re spatial derivatives and ling the at ar
inte mios coa ley ae fe ae n
Gets ende ee Decor to cage
28 chapter? ne Yan
Combining this wih he time den
reer?
he tremens ie wa uation Noe Ut x
‘and do appear yammetals nd he fori ech
‘by intoducia e Laplacian operator
TA es
crean it somes simply
tin. The factions fan, which ae eis diferido ae
whee Cn Cs sve,
fe, we sth ots be hse so EE testing she.
2.9 Spherical Waves
ST Ts
wheter. 0. dae defined by
Combining this wih he time den
reer?
he tremens ie wa uation Noe Ut x
‘and do appear yammetals nd he fori ech
‘by intoducia e Laplacian operator
TA es
crean it somes simply
tin. The factions fan, which ae eis diferido ae
whee Cn Cs sve,
fe, we sth ots be hse so EE testing she.
2.9 Spherical Waves
ST Ts
wheter. 0. dae defined by
Amrindoó, yerin@snd, cared
ras, manos Ut are spray symmetrical 6 one at
Tes Laptcanor thn Imp
sys Life) as
(6, Sir wi the Casan form ofthe Laplcin. Ex
SD perse tn the spherically yes! wavetuttin
amet each om to polar coors. Examintns
FM ETE a8 ar
ae Hoyo
= )- (1-3)
Thisroulecan be eres
29 Some: 29
This sepresnisa spherical wave progress
ras, manos Ut are spray symmetrical 6 one at
Tes Laptcanor thn Imp
sys Life) as
(6, Sir wi the Casan form ofthe Laplcin. Ex
SD perse tn the spherically yes! wavetuttin
amet each om to polar coors. Examintns
FM ETE a8 ar
ae Hoyo
= )- (1-3)
Thisroulecan be eres
29 Some: 29
This sepresnisa spherical wave progress
ober ttm osa nike pulse a wo diferent umes as e mane expands var
the plane wave, chenal wave decrease in ampltae Renee th hese resis ou sn esd ofthe
hc origin Figure 2 28 lac hs ropa y show sve draun omnis mae, ier than a pol in Fis
propage ut. aus res
the plane wave, chenal wave decrease in ampltae Renee th hese resis ou sn esd ofthe
hc origin Figure 2 28 lac hs ropa y show sve draun omnis mae, ier than a pol in Fis
propage ut. aus res
away rom he our, smal ea of the wave
postion ofa plane wate (Fa
{font vill cose sesemble
Weil ns
rely examin another delire warefom. he
ar eyiider Uforuntel a preche mathe:
ent fartoo involved o o here We sl ine
The simple case ofeylindical symmetry requires that
The Bindegendence means thats plan perpendicalarto the
anew intersect the wavetontin acl, MR ma vay
ferent value of «In édition, he inde pendenc for
Fee 2.27 The una one corea
cl IE.
De found a there wer o
ne IE
4 atopaque ren
postion ofa plane wate (Fa
{font vill cose sesemble
Weil ns
rely examin another delire warefom. he
ar eyiider Uforuntel a preche mathe:
ent fartoo involved o o here We sl ine
The simple case ofeylindical symmetry requires that
The Bindegendence means thats plan perpendicalarto the
anew intersect the wavetontin acl, MR ma vay
ferent value of «In édition, he inde pendenc for
Fee 2.27 The una one corea
cl IE.
De found a there wer o
ne IE
4 atopaque ren
32 Chapter 2 iow
PROBLEMS
PROBLEMS
Five P214
Faure 215
Faure 215
LA When np i Concise erario
28 want ET
Fran 35
245° Maks apta Ayo ma
246" Mic op stale with col wy vai of rum
27" Wid hes pren in ain e po
28 want ET
Fran 35
245° Maks apta Ayo ma
246" Mic op stale with col wy vai of rum
27" Wid hes pren in ain e po
Electromagnetic
Theory, Photons,
and Light
Theory, Photons,
and Light
ingly smoot and canon Dow. The eh
a masse i pedicle foe day tay, a
moon of eich commer fs nimporte
Observer. The ergy transported by «luge number of ph
tons ton he average, quvalento the energy tastes.
caca electromagnet wave. For these tons e ca
Su el representation of eletomapnetc phenome Bak
een, and wil continue od, seul None, hou
msn waves ton ofthe mocrocopie worl jst ar
{he apprent conimau naar of ordinary mater à fie
‘Quite progmutially. then. we can consider Hitt to e à
‘asic eletomagnci wave, Apia in mind a ere are
Sitios for which his descriptions woefully inadequate
3.1 Basic Laws of Electromagnetic
Theory
‘Orient in hs section ist review and deve
ess needed 10 appreciate the concept of slectomagneti
"We know rom experiment Ba charges, even out ep
arsed in vacuum experience a muta! nercin. Rel the
fms letras demonstration in which pi al
‘Sm senses te pretence of hago vo tu
that each charge mis (and absorbs) uscar af uadetected
ailes termal photons) The exchenge of these prices
Among the charges may be regaded as the mode of interac
a Base Let
re eras directly with he lest edi whic is
nee. Tux ia pont ch joer
cid abs position hes
in adien. we serve tha
ze,
ESS tores E, and F, ocur concurrent he
nd net es, whereupon F FEU
Avwetses electo fis ate generated by th esc
ds. Tis interdependence of F and Bis key pict
ine décrite of ight
F
3.1.1 Faraday's Induction Law
Mice Faraday ted in is noehonk in 1922, challenge he
set him with un easy confidence tha made seem o,
sable Aer several ca doing otr ewer, Faraday
returned tthe problem. eit induction in 1831
His is apparatus mage its mounted on à mod
en spot ig 3) One, ale the primar. as tached o
komo. He found tht he plvanomerdfscted
caring o zo rt ma, dsp ths co
a masse i pedicle foe day tay, a
moon of eich commer fs nimporte
Observer. The ergy transported by «luge number of ph
tons ton he average, quvalento the energy tastes.
caca electromagnet wave. For these tons e ca
Su el representation of eletomapnetc phenome Bak
een, and wil continue od, seul None, hou
msn waves ton ofthe mocrocopie worl jst ar
{he apprent conimau naar of ordinary mater à fie
‘Quite progmutially. then. we can consider Hitt to e à
‘asic eletomagnci wave, Apia in mind a ere are
Sitios for which his descriptions woefully inadequate
3.1 Basic Laws of Electromagnetic
Theory
‘Orient in hs section ist review and deve
ess needed 10 appreciate the concept of slectomagneti
"We know rom experiment Ba charges, even out ep
arsed in vacuum experience a muta! nercin. Rel the
fms letras demonstration in which pi al
‘Sm senses te pretence of hago vo tu
that each charge mis (and absorbs) uscar af uadetected
ailes termal photons) The exchenge of these prices
Among the charges may be regaded as the mode of interac
a Base Let
re eras directly with he lest edi whic is
nee. Tux ia pont ch joer
cid abs position hes
in adien. we serve tha
ze,
ESS tores E, and F, ocur concurrent he
nd net es, whereupon F FEU
Avwetses electo fis ate generated by th esc
ds. Tis interdependence of F and Bis key pict
ine décrite of ight
F
3.1.1 Faraday's Induction Law
Mice Faraday ted in is noehonk in 1922, challenge he
set him with un easy confidence tha made seem o,
sable Aer several ca doing otr ewer, Faraday
returned tthe problem. eit induction in 1831
His is apparatus mage its mounted on à mod
en spot ig 3) One, ale the primar. as tached o
komo. He found tht he plvanomerdfscted
caring o zo rt ma, dsp ths co
38. Copter 3 cromo Pos ve
fi
Faraday wound two coils around oppasing sections of
a sof ron rg (Fig. 3.1). Now the effect was univ
ia changing magnetic field generated a current
Indeed as he would coniue to discover. change vas the
By ing mage mo a coi, Pasay HO
Ima re oremf--seos he coils termina (este
aa aol nd js we rl) Fute
moved The duced em depende on he ne ofschange of D
through te coil and noo lA weak magoet moved
When he same changing Bild pases trough toi
Fern wire ops sin Fig 32, he induced em
cross he ras af he Layer loop. I sos, ers
‘shore the cé changing, e induced en i proportion
cli are À th loop penetrated perpenicaary y he
Fe. Mt
2 À cos A and, when # = 90, the Induced emf is zero
38/37 = emi A,. The cunver slo Rods when the
els content, the induced emf i proportional tthe rate.
change ofthe perpendicular area penetrated a co
Amir rot ar even squashed whiten conn ih
fore 32 Ainge ino
PTA À mere
‘Mans when à RAA
Nit Fes a heel pods on eo:
stung of bth À, nd that on be ao change of thie
proc. This shou bring to mind he non of the x of the
eld the product of Seda
Through the wie loops
aca besote penetrations
he Max of the magneti cid
More seer, vrs in ace si kel othe of
the magnets Held through any open ares À Bound by 1
5
fi
Faraday wound two coils around oppasing sections of
a sof ron rg (Fig. 3.1). Now the effect was univ
ia changing magnetic field generated a current
Indeed as he would coniue to discover. change vas the
By ing mage mo a coi, Pasay HO
Ima re oremf--seos he coils termina (este
aa aol nd js we rl) Fute
moved The duced em depende on he ne ofschange of D
through te coil and noo lA weak magoet moved
When he same changing Bild pases trough toi
Fern wire ops sin Fig 32, he induced em
cross he ras af he Layer loop. I sos, ers
‘shore the cé changing, e induced en i proportion
cli are À th loop penetrated perpenicaary y he
Fe. Mt
2 À cos A and, when # = 90, the Induced emf is zero
38/37 = emi A,. The cunver slo Rods when the
els content, the induced emf i proportional tthe rate.
change ofthe perpendicular area penetrated a co
Amir rot ar even squashed whiten conn ih
fore 32 Ainge ino
PTA À mere
‘Mans when à RAA
Nit Fes a heel pods on eo:
stung of bth À, nd that on be ao change of thie
proc. This shou bring to mind he non of the x of the
eld the product of Seda
Through the wie loops
aca besote penetrations
he Max of the magneti cid
More seer, vrs in ace si kel othe of
the magnets Held through any open ares À Bound by 1
5
We sould not. however, gt oo involved with the image of
‘sites and cient an em O present sonsem i wih the
ee and magnet els themselves.
In very general terms, an emia potential ifrese, and
‘ialenergy difference per unt charge coresponds to work
(me pe tit charge. whichis force per uk charge tines di
tance and thas elect ed times distance. The emf exists
only asa rest fe presence aan lc el:
ent =f Bad
taken around the closed curve €, comesponding 0 te loop
Eepnting Eqs (32) and (3.3), and making use of kg.
. $ Est
We began this discussion y examining a conducting top,
and have avd at Eg, (2.4: this expression excep for the
ut € onains no reference wo the physical op. In facı he
Path can be chosen abia and need na De wo, or any
Sere eae, a conducir The elect Bld in a, (3) aies.
fet fom the presence of elects charges Bu ae rom he
fe ink. the field lines close on themselves, forming loops
res
‘We ae interested in electromagnetic waves trveing in
space where there are no wie loops, andthe magne lox
Changes because changes. The duction Lan (Eq. 3.4 can
us
sn
A para deivaiv with respect 1 4 taken because e
sony also à funcion of te suce vara. This expres
fime-voring magnet ld vil have an electri field avr
‘lated wth
3.1.2 Gausss Law—Electric
noes fundamental aw of electromagnetism is named afer
‘he era muhemaichn Kal Friedrich Gat (17771858)
‘Guus’ Laws about the relationship between he Mux ofthe
lest arte sources of ha Nox. charge, Te ess
ee from Nut dynamic wher both te oncep ft
nd fox ere introduzca. The low ofa Mud as prose
sie cds pictured wa il Ines Figure 2. shows apor
Tom of a moving id within which er a eon slated
{fluc Av). is he volume of id owing pasta point in he
ube per ni ime, The volume Mux GEN BE us
‘sites and cient an em O present sonsem i wih the
ee and magnet els themselves.
In very general terms, an emia potential ifrese, and
‘ialenergy difference per unt charge coresponds to work
(me pe tit charge. whichis force per uk charge tines di
tance and thas elect ed times distance. The emf exists
only asa rest fe presence aan lc el:
ent =f Bad
taken around the closed curve €, comesponding 0 te loop
Eepnting Eqs (32) and (3.3), and making use of kg.
. $ Est
We began this discussion y examining a conducting top,
and have avd at Eg, (2.4: this expression excep for the
ut € onains no reference wo the physical op. In facı he
Path can be chosen abia and need na De wo, or any
Sere eae, a conducir The elect Bld in a, (3) aies.
fet fom the presence of elects charges Bu ae rom he
fe ink. the field lines close on themselves, forming loops
res
‘We ae interested in electromagnetic waves trveing in
space where there are no wie loops, andthe magne lox
Changes because changes. The duction Lan (Eq. 3.4 can
us
sn
A para deivaiv with respect 1 4 taken because e
sony also à funcion of te suce vara. This expres
fime-voring magnet ld vil have an electri field avr
‘lated wth
3.1.2 Gausss Law—Electric
noes fundamental aw of electromagnetism is named afer
‘he era muhemaichn Kal Friedrich Gat (17771858)
‘Guus’ Laws about the relationship between he Mux ofthe
lest arte sources of ha Nox. charge, Te ess
ee from Nut dynamic wher both te oncep ft
nd fox ere introduzca. The low ofa Mud as prose
sie cds pictured wa il Ines Figure 2. shows apor
Tom of a moving id within which er a eon slated
{fluc Av). is he volume of id owing pasta point in he
ube per ni ime, The volume Mux GEN BE us
‘sequal in magna lows gersscond lows out pet
med orale ras eae ze how
To apply these ies 10 theo
ed ea A pce in some airy lo el,
Fi. 37 The Man of elie Hl rough is
wf
The ck dub grass a eminde ta th u
‘normal. When there are no sources or sinks of the electric
ed hin the region encompased by the coed surface
the net through the surface equals zern na much sa
cd. consider an
- 26 ana ot ts on
be
ewe 37 tot
Mn à ce A
radis rceterod on and surounding postive point-charge
(a. im vacuum The Es everywhere out edi,
nat any inc tirer perpendicular the wae
a be GRE ou af ie weg
Bet we know fon: Coulomb's Law tha the point charge as
trae up of pont sng. ASE tthe e on de
cers mme of changes card with say closed se 8
y
med orale ras eae ze how
To apply these ies 10 theo
ed ea A pce in some airy lo el,
Fi. 37 The Man of elie Hl rough is
wf
The ck dub grass a eminde ta th u
‘normal. When there are no sources or sinks of the electric
ed hin the region encompased by the coed surface
the net through the surface equals zern na much sa
cd. consider an
- 26 ana ot ts on
be
ewe 37 tot
Mn à ce A
radis rceterod on and surounding postive point-charge
(a. im vacuum The Es everywhere out edi,
nat any inc tirer perpendicular the wae
a be GRE ou af ie weg
Bet we know fon: Coulomb's Law tha the point charge as
trae up of pont sng. ASE tthe e on de
cers mme of changes card with say closed se 8
y
Combining we xo equations fr aw
$
hang distibtion ac bin soninaous Then tho volum
not by 43 Va the charge ibn ha à demi
8-150
Electric Permitivty
east? 10
{yl appear in Eine of ey One function ofthe
Bat the concept e base o the desertion f he paral plat
capacitor (ee Section 2.1.9, There the medium depen
nd de gee Carat. Wed I ofen mear
ty a procedure in whic the material under study de paced
win capacitor Conceptual. te permito emadies
te lela ben ofthe medium.
‘ystems, wich was, u best, a waste of dime, The same
gravity i... demi ratios). Thus was advantageous 10 lb
tite values nt obit a ered qui tht si
Pendent of the system of unis Being ase. According, we
ine Kase. Tis is the dire constant or le
“of x material can then be expressed in terms of cas
u itresi ips te arta the privi
ed 1 the spce of igh in electric material, such a
Bess ar and quar
3.1.3 Gauss' Law—Magnetic
Theres no oan magnetic cour he elec hare
est extensive searing ex in orar sl samples Uni
the let Hed e msi eB doc ot ver I
Source orsink Magnetic felts abe described in term of
comen diode we igre io
ering and crio hom (ig. 38). Thi
he magnate equivalent of Caves Lan
ean we have 1e na
afro a
3.1.4 Ampöre's Circuital Law
wih Andre
sta doing ojos bai’ wort . Ar te
Ec surrounding i (Fig 39). We kaw Trom crimes
OC SN wt CIA
he greet Gr when twas come e nk map
$
hang distibtion ac bin soninaous Then tho volum
not by 43 Va the charge ibn ha à demi
8-150
Electric Permitivty
east? 10
{yl appear in Eine of ey One function ofthe
Bat the concept e base o the desertion f he paral plat
capacitor (ee Section 2.1.9, There the medium depen
nd de gee Carat. Wed I ofen mear
ty a procedure in whic the material under study de paced
win capacitor Conceptual. te permito emadies
te lela ben ofthe medium.
‘ystems, wich was, u best, a waste of dime, The same
gravity i... demi ratios). Thus was advantageous 10 lb
tite values nt obit a ered qui tht si
Pendent of the system of unis Being ase. According, we
ine Kase. Tis is the dire constant or le
“of x material can then be expressed in terms of cas
u itresi ips te arta the privi
ed 1 the spce of igh in electric material, such a
Bess ar and quar
3.1.3 Gauss' Law—Magnetic
Theres no oan magnetic cour he elec hare
est extensive searing ex in orar sl samples Uni
the let Hed e msi eB doc ot ver I
Source orsink Magnetic felts abe described in term of
comen diode we igre io
ering and crio hom (ig. 38). Thi
he magnate equivalent of Caves Lan
ean we have 1e na
afro a
3.1.4 Ampöre's Circuital Law
wih Andre
sta doing ojos bai’ wort . Ar te
Ec surrounding i (Fig 39). We kaw Trom crimes
OC SN wt CIA
he greet Gr when twas come e nk map
# A Figure 39 The Bi suroundng
tc cane a) Les deine hi monopole barges th
experiences force when paced in a magieti el quo
donc i th poses Since Ie direcion of the force chan
became changes dienten. we will have to divide the ce
One eat, Wok isthe component fhe For parle ot
placement neste ipacement AN = 4.8, and
‘everywhere vangent to the path, so hat By = B= ya/ 2
Mw abate fr B the ile cuen expresion
which varies vrs with the ra cancel he wok ie
independent of the etal pth ake. Since no work dove
bn wave perpendicular a Bhs work mus hehe sume
weave fot away from he wie oe in toward hy along
ration, camino
Work wil be the same for any o
Ping me cum exprwin for and casing
The magna charge has appre, which mie inc ve
iment win a monepee SU the physics was comustem aná
hc equation shoul old, monopole or, Moreover, hee
ral curry
path th
1 mires cacompasd y he coe
ge wil superimpoe und add, pci a er
Str fre parte ids and mus Be
$5
Tobi equations Known es Ame aw. dough
one tei was commonly refered 1 a ie "work ul
the wal cura psi win te comes of
Fe po ne negro ser he aa
iat pf Fas am
sa by i. 2.10) The quiz
Nat Cr Who he cment ins ina mac
TT gue 310 Come ty
tc cane a) Les deine hi monopole barges th
experiences force when paced in a magieti el quo
donc i th poses Since Ie direcion of the force chan
became changes dienten. we will have to divide the ce
One eat, Wok isthe component fhe For parle ot
placement neste ipacement AN = 4.8, and
‘everywhere vangent to the path, so hat By = B= ya/ 2
Mw abate fr B the ile cuen expresion
which varies vrs with the ra cancel he wok ie
independent of the etal pth ake. Since no work dove
bn wave perpendicular a Bhs work mus hehe sume
weave fot away from he wie oe in toward hy along
ration, camino
Work wil be the same for any o
Ping me cum exprwin for and casing
The magna charge has appre, which mie inc ve
iment win a monepee SU the physics was comustem aná
hc equation shoul old, monopole or, Moreover, hee
ral curry
path th
1 mires cacompasd y he coe
ge wil superimpoe und add, pci a er
Str fre parte ids and mus Be
$5
Tobi equations Known es Ame aw. dough
one tei was commonly refered 1 a ie "work ul
the wal cura psi win te comes of
Fe po ne negro ser he aa
iat pf Fas am
sa by i. 2.10) The quiz
Nat Cr Who he cment ins ina mac
TT gue 310 Come ty
ee
‘ied is bounded bythe curve C. which make for an oi
31a. flat are Ay isused, a et current of ows through it
and thee de a eld song curve €. The Hight sie of Fa
(G0) onze, the elt sd nonzero, BY are den
wed nad 1 compas €. at euren pases tought
Sethe Field mast now be ero, even howa noi phat
scaly changed. Samen is obviously wrong
Moving lares are ote only Source of a magnet il
‘ile charging or dischrging a capacitor, one can measure a
indisinguishahle from the feld surrounding the leads, even
Note, however hat Ai the are ofeach plate ard the
@
‘naive of both sides il.
hic etotsely eurent dns ames Clerk Manvel
hypothesized the existence of ust such à mechan, whic
fiar [Eje
ven hen = 0 atimenaping Efe wil be accompanied
bya feta ty 37
3.1.5 Maxwells Equations
The tof nigral expressions given by ES.)
and (3.13) have come to be known a Maxwell Equation»
Remember thr these ae generalizations of experimental
{plist the behavior ofthe electric and magnets fle in
Tre ce. ee = eo, a Bah pan Saro
hs insane
eus
un
sis a exp or mula sal, ie ee
‘Sommer, However affect BB wil nt lic E, The
tree sem implica good des a ys am
Mae Equation cam he writen in diferent orn
ich wll be somewhat more aseo for our purposes. The
‘ied is bounded bythe curve C. which make for an oi
31a. flat are Ay isused, a et current of ows through it
and thee de a eld song curve €. The Hight sie of Fa
(G0) onze, the elt sd nonzero, BY are den
wed nad 1 compas €. at euren pases tought
Sethe Field mast now be ero, even howa noi phat
scaly changed. Samen is obviously wrong
Moving lares are ote only Source of a magnet il
‘ile charging or dischrging a capacitor, one can measure a
indisinguishahle from the feld surrounding the leads, even
Note, however hat Ai the are ofeach plate ard the
@
‘naive of both sides il.
hic etotsely eurent dns ames Clerk Manvel
hypothesized the existence of ust such à mechan, whic
fiar [Eje
ven hen = 0 atimenaping Efe wil be accompanied
bya feta ty 37
3.1.5 Maxwells Equations
The tof nigral expressions given by ES.)
and (3.13) have come to be known a Maxwell Equation»
Remember thr these ae generalizations of experimental
{plist the behavior ofthe electric and magnets fle in
Tre ce. ee = eo, a Bah pan Saro
hs insane
eus
un
sis a exp or mula sal, ie ee
‘Sommer, However affect BB wil nt lic E, The
tree sem implica good des a ys am
Mae Equation cam he writen in diferent orn
ich wll be somewhat more aseo for our purposes. The
88 Chapter 3 Seem Tey, Pion rat
faa =
ñ E,
RCE qn em
5% a
The rando ha has een made from the formulation of
ha need to comprehend mi
ce proces whereby sic and noe els means
3.2 Electromagnetic Waves _
penalty te eee sony af Manoel
Tom and ir metete E ad nth ego,
Tos por urethanes ote we
Sa uc E ange ie SR e
A AA
‘hanes thy 03, Coon, ne mea te
ii mur te tog odos
sant radial ic extending nal iestons pe
rio propagates ou ino pace some finite spend The
Secar levine cd induces «maga eld by means
fof Fg (218) oF 319). charge vel constant the
faa =
ñ E,
RCE qn em
5% a
The rando ha has een made from the formulation of
ha need to comprehend mi
ce proces whereby sic and noe els means
3.2 Electromagnetic Waves _
penalty te eee sony af Manoel
Tom and ir metete E ad nth ego,
Tos por urethanes ote we
Sa uc E ange ie SR e
A AA
‘hanes thy 03, Coon, ne mea te
ii mur te tog odos
sant radial ic extending nal iestons pe
rio propagates ou ino pace some finite spend The
Secar levine cd induces «maga eld by means
fof Fg (218) oF 319). charge vel constant the
no Sted ne ete e
de ae edt pie mor mon
il an mone appropriately be considered
eden oft, Bound together a a single city the time
an endless cycle The electromagnetic waves reaching vt
from he elaivly nearby Andromeda galaxy (which ea e
sso with he naked ee) have bee onthe wing for 2 200000
(in wth respect to the consent feds. Notice, however,
‘atthe igh depres of symm in Masel’ tition for
fee space suggests thatthe disturbance will propagate ln a
“cion tha is ymmetial ( both E and. That implies
tan electromagnetic wave canot be purely longitudinal
ie. astong sE and Bate nat parle Lets now replace
rieur ith bit of auton
pends [shows that Manell's Equations for fee space
canbe manipulaed ¡no the form of two extremely conexo
Een tano
= SEE cou SE tar
The Laplcian * 7%, operates on cach compo of E aná,
stat the wo veto equations actly pesca tl ? six
PE = Wee jur shee
scalar equations, In Canesian coordina,
Fe 2
an, PI
da. 20, #8, %,
Expression of this om, ich atthe pace and time
ations of some physical quanti had bee tie lon belore
Masses work and were know 1 describe wave phenome
ma. 28) Each and every component o he electomagntic
field eB BB eye te Scala diferent) wave
Stun
ee 1 #8
à Le pen
o evalune 5, Maxwell made use of he eu fiat
sperme ecfomedt 156 o Lesprig by Wiel Weber
fase and Reda Kohtrasch (ap Be. rat
Rent, poncdaye jis ancla valve of te 710
mag Cin ni and until recent one mg determine e
‘ety rom simple capacitor meuturemeni, any event
A now the moment ft in fre space the profited
de ae edt pie mor mon
il an mone appropriately be considered
eden oft, Bound together a a single city the time
an endless cycle The electromagnetic waves reaching vt
from he elaivly nearby Andromeda galaxy (which ea e
sso with he naked ee) have bee onthe wing for 2 200000
(in wth respect to the consent feds. Notice, however,
‘atthe igh depres of symm in Masel’ tition for
fee space suggests thatthe disturbance will propagate ln a
“cion tha is ymmetial ( both E and. That implies
tan electromagnetic wave canot be purely longitudinal
ie. astong sE and Bate nat parle Lets now replace
rieur ith bit of auton
pends [shows that Manell's Equations for fee space
canbe manipulaed ¡no the form of two extremely conexo
Een tano
= SEE cou SE tar
The Laplcian * 7%, operates on cach compo of E aná,
stat the wo veto equations actly pesca tl ? six
PE = Wee jur shee
scalar equations, In Canesian coordina,
Fe 2
an, PI
da. 20, #8, %,
Expression of this om, ich atthe pace and time
ations of some physical quanti had bee tie lon belore
Masses work and were know 1 describe wave phenome
ma. 28) Each and every component o he electomagntic
field eB BB eye te Scala diferent) wave
Stun
ee 1 #8
à Le pen
o evalune 5, Maxwell made use of he eu fiat
sperme ecfomedt 156 o Lesprig by Wiel Weber
fase and Reda Kohtrasch (ap Be. rat
Rent, poncdaye jis ancla valve of te 710
mag Cin ni and until recent one mg determine e
‘ety rom simple capacitor meuturemeni, any event
A now the moment ft in fre space the profited
‘peed of al eletomagnsi waves would the Be
“This Mcortical value was in remarkable agreement withthe
previousy measured speed of ph 1313 300s eter
rumen 1339 with ora tod whl wre avala
Fest pr ery
is bia amas as ne of the gat net
ped of lig in vacuum byte syabol which comes fom
{he Lain word cele meaning fst. In 1983 the 17 Con
ein of the meer nd rey xed te pes of Tt
3.2.1 Transverse Waves
The experimental veifidranssene charactor fight mu
om be explinsd within he como sl elstuumagnetie theo
19. Toth e, con erh al ample cs fa plane war
propagan ic inthe potes dretion The cts
Felines a tion o Es. (AI 283 er Ex ont
‘ve cach of afte set of plane perpendicular vo
asin Its erfor a funcion only ol nd that E
Ein. We now refer ack to Maswell's Equations and ia
particular to E, (321) which is general) wad as he diver
Fence of E gual srr Sine À NEO
fx ans af: bt coun ts pl cnr i
ave = Othe roman wave has no lect field
ons dci el pospaon Tee ld ao
cd th he pam nave exce me
meh Wey Gu wae oe wl ane Uc D
tome rome eco of, Sacha don cn
nds e iaa De ho nd Bed
hap Whoa ay Io olga. der va
as vo that he elect ie is paral to the ras where
B= lean 025
Therefore Band 8 are constant and of interet at present
In me dependent eld can only have a component inthe
direction, Clea ten. in fre space, he plane electromag.
etc wave ie mantierse (Fi. 313. xcept inthe as for
tal cence, Auch wave propagating in el mater! mea
An general ot tanwerse—acomplcon ang fom the
fa athe medium maybe diste ar conan re charge.
‘We have not specified he form ofthe distance other
thant say that a plan ave Our conclusions ae there
Tone quite general, applying equally well Both pales and
“This Mcortical value was in remarkable agreement withthe
previousy measured speed of ph 1313 300s eter
rumen 1339 with ora tod whl wre avala
Fest pr ery
is bia amas as ne of the gat net
ped of lig in vacuum byte syabol which comes fom
{he Lain word cele meaning fst. In 1983 the 17 Con
ein of the meer nd rey xed te pes of Tt
3.2.1 Transverse Waves
The experimental veifidranssene charactor fight mu
om be explinsd within he como sl elstuumagnetie theo
19. Toth e, con erh al ample cs fa plane war
propagan ic inthe potes dretion The cts
Felines a tion o Es. (AI 283 er Ex ont
‘ve cach of afte set of plane perpendicular vo
asin Its erfor a funcion only ol nd that E
Ein. We now refer ack to Maswell's Equations and ia
particular to E, (321) which is general) wad as he diver
Fence of E gual srr Sine À NEO
fx ans af: bt coun ts pl cnr i
ave = Othe roman wave has no lect field
ons dci el pospaon Tee ld ao
cd th he pam nave exce me
meh Wey Gu wae oe wl ane Uc D
tome rome eco of, Sacha don cn
nds e iaa De ho nd Bed
hap Whoa ay Io olga. der va
as vo that he elect ie is paral to the ras where
B= lean 025
Therefore Band 8 are constant and of interet at present
In me dependent eld can only have a component inthe
direction, Clea ten. in fre space, he plane electromag.
etc wave ie mantierse (Fi. 313. xcept inthe as for
tal cence, Auch wave propagating in el mater! mea
An general ot tanwerse—acomplcon ang fom the
fa athe medium maybe diste ar conan re charge.
‘We have not specified he form ofthe distance other
thant say that a plan ave Our conclusions ae there
Tone quite general, applying equally well Both pales and
AS IES We Re MEM pone eur ar ar
he eapresed ner of sinusoidal waves using Fourie
moni waves and wit Ese tae
ing Fa. 8.2,
fs density an de fond by irc o
me _—
Wing Fa (328) ve bein
wo es r= afer a 629
The conan ig which eprsct tienden
den fed. has been disrezarded Comparison uf a seat
hy Cakes VA at
B=. em
1. if only ya ae, ad ave te sum
en
19 Maxwell's Equnons- Ar we a in he previos chuter
stich are da and peal waves F315)
3.3 Energy and Momentum
‘wane i that ramp
‘Hom Gen the are at Bond th
lion mist zsch ne ar, yet il
do work othe electots within your y
3.3.1 The Poynting Vector
Any coctromogocti ware exis wihin some reg
and vi Weteore mural consider ie radiant eras Pe
aie or psi
mes oc emer density
‘este snc pas othe fl
he eapresed ner of sinusoidal waves using Fourie
moni waves and wit Ese tae
ing Fa. 8.2,
fs density an de fond by irc o
me _—
Wing Fa (328) ve bein
wo es r= afer a 629
The conan ig which eprsct tienden
den fed. has been disrezarded Comparison uf a seat
hy Cakes VA at
B=. em
1. if only ya ae, ad ave te sum
en
19 Maxwell's Equnons- Ar we a in he previos chuter
stich are da and peal waves F315)
3.3 Energy and Momentum
‘wane i that ramp
‘Hom Gen the are at Bond th
lion mist zsch ne ar, yet il
do work othe electots within your y
3.3.1 The Poynting Vector
Any coctromogocti ware exis wihin some reg
and vi Weteore mural consider ie radiant eras Pe
aie or psi
mes oc emer density
‘este snc pas othe fl
compare thin a ane ami toria)
waves: montes, 1% quie general a is applicability
The energy streaming through space in he form o an ele
"romagnat waves shared equals Bebeen Ihe consent
‘etic and magnetic li. ssh
india some te AA) wil eon Than
thatthe ene lo m the Seton ofthe propagan oe
MO ee th
he magnitude of is he power ger ui arc ron a sur
face whore nal i pall 18. Named air John enr)
{humo nca polarize dons of Band
A AS
Be fem as sie
ci cinco
on of energy per it area per at
‘Averaging Harmonie Functions
waves: montes, 1% quie general a is applicability
The energy streaming through space in he form o an ele
"romagnat waves shared equals Bebeen Ihe consent
‘etic and magnetic li. ssh
india some te AA) wil eon Than
thatthe ene lo m the Seton ofthe propagan oe
MO ee th
he magnitude of is he power ger ui arc ron a sur
face whore nal i pall 18. Named air John enr)
{humo nca polarize dons of Band
A AS
Be fem as sie
ci cinco
on of energy per it area per at
‘Averaging Harmonie Functions
idly varia fin fine ned ic as ga the
fs, sine cosine-squared has double the frequency of
cna) Theseforo, ls ineamanecas vals _mosid be a
pcia! quan o measure dic. This suggest at
san energy during some fte ¡nieva ol me sing, for
‘ample a photocell late, orbe resina of a human
y harmonic fonctions, suggest that we take a moment 10
Sindy e average values of sh intone. The me vergel
‘ale of some funenon it over am intere! Ts wien 3
Toe resulting value of tr very much depends on 7. To.
“Tae premiar should remind wtp 22) 0F si wi?
ewe
moe or F
‘The rai in bracket so common and import in Optics
that ts given o om name: (in a) a called ne Tie
Inge veal an ray pats oe above expression ek
“Te vegas ing il de
same egy having ans fons ampli at drops
‘trom inal vale of LO very rapidly (ig 3.17 a Tabe
Tithe Appendix) Sine sinew = Data a) 2= 2 which
happens when T= = itfllows hu co wr averaged over an
eral T equa to one period equals er. Simi, cs a
fot That's eaonable that exch of hese functions encor
Bew the ats and tha’ wat the defining nega come
sponds o. After an interval
‘il beso mal shat he Mutton round er sl be ep
fs, sine cosine-squared has double the frequency of
cna) Theseforo, ls ineamanecas vals _mosid be a
pcia! quan o measure dic. This suggest at
san energy during some fte ¡nieva ol me sing, for
‘ample a photocell late, orbe resina of a human
y harmonic fonctions, suggest that we take a moment 10
Sindy e average values of sh intone. The me vergel
‘ale of some funenon it over am intere! Ts wien 3
Toe resulting value of tr very much depends on 7. To.
“Tae premiar should remind wtp 22) 0F si wi?
ewe
moe or F
‘The rai in bracket so common and import in Optics
that ts given o om name: (in a) a called ne Tie
Inge veal an ray pats oe above expression ek
“Te vegas ing il de
same egy having ans fons ampli at drops
‘trom inal vale of LO very rapidly (ig 3.17 a Tabe
Tithe Appendix) Sine sinew = Data a) 2= 2 which
happens when T= = itfllows hu co wr averaged over an
eral T equa to one period equals er. Simi, cs a
fot That's eaonable that exch of hese functions encor
Bew the ats and tha’ wat the defining nega come
sponds o. After an interval
‘il beso mal shat he Mutton round er sl be ep
the lite. After enough
les the tea under the fi coro
3.3.2 Irradiance
to something called the radiance +
Any hind of il deis has a eta window ha
received. st depend ca Lands hero of imite iy
however the Fi now divided om. gl pal amy
ana pr mime, ah
pci case of harmonic Helv md in Qu
the mapinnde of the
Bo xR oe eh — an
Because en = a) = for >> esse Problem 32
The radiance proportions ote square of te apie
‘ofthe seco eld. Pwo mA ways yng we ne
La as
‘Sin ote Iman comes
T= ex), am
Since we have amet: E ivconsidenbly me five at
vein forces nd doin work om charges than Be bal
toler to en the optical field ad se 346) aos er
‘rely
The tine ae of bw dia nergy the tl paw
er Por radiant Max, generally expressed in wat. I we
‘vide the rain Ma nde ono xing to ute y
(Wa Be Trier ce we pea OE alice ME
{ater tance an in citrine the x deny. The
The Invorse Square Law
Wera eter thatthe sphere ave alton othe der
it Let snow examin thi same tre within he ont
fre space, min energy equi inal tection 1. emi
FI Lat ad Freres the apices e
enh sach ace or seco mus be eau soe sere ee
lc ampltod mus desp onen with The iad
les the tea under the fi coro
3.3.2 Irradiance
to something called the radiance +
Any hind of il deis has a eta window ha
received. st depend ca Lands hero of imite iy
however the Fi now divided om. gl pal amy
ana pr mime, ah
pci case of harmonic Helv md in Qu
the mapinnde of the
Bo xR oe eh — an
Because en = a) = for >> esse Problem 32
The radiance proportions ote square of te apie
‘ofthe seco eld. Pwo mA ways yng we ne
La as
‘Sin ote Iman comes
T= ex), am
Since we have amet: E ivconsidenbly me five at
vein forces nd doin work om charges than Be bal
toler to en the optical field ad se 346) aos er
‘rely
The tine ae of bw dia nergy the tl paw
er Por radiant Max, generally expressed in wat. I we
‘vide the rain Ma nde ono xing to ute y
(Wa Be Trier ce we pea OE alice ME
{ater tance an in citrine the x deny. The
The Invorse Square Law
Wera eter thatthe sphere ave alton othe der
it Let snow examin thi same tre within he ont
fre space, min energy equi inal tection 1. emi
FI Lat ad Freres the apices e
enh sach ace or seco mus be eau soe sere ee
lc ampltod mus desp onen with The iad
Figure 319. Te geeneny ol he nese Sa La.
well known Inverse Square Law. which is easily vetted
‘il point source and à photographic exposure mete
3.3.3 Photons
Light sbsoehed and mid in ing dirt hart in par
cles of electromagnetic"Mull.” known x photons. That much
ts been confirmed ands well ewablshed, ut he question
‘of whether or os light is el” a stream of photons ae
frm ted it hat sue Wi be tevin vera Ges
Ordinaria light beam delivers many minute energy
ana at erent grrr natures oly hdc und à
Ésminoous phenomenon is observed macroscopically. That
Som of bin i commonplace in Nature e forces exerted by
(beindiidn gus molecules in a wind blend nto what sens
Sonia presore, butt obvogsy Indeed Bar nal
‘ogy beeen à gas and à Now of photons ise we will come
taco present
A AE great French lic LOU de Broglie pt
‘Light im sor hemos fined form of mate,” and all
mater, including light, fe quamzed. At base e comes in
minute elementary uni qurks,Ioptons, and photons, That
‘overarching un is among the most appealing encon 10
mac Ih photon as parco (whatever à "pail 1)
The Failure of Classical Theory
In 1900 Max Planck produced a rather etait, nd some
what eroneois, analysis ofa process Known as Mack
radiation p. SD. Nonetheless, the expression he same ap
‘ith betty al he exis experiment dat, fst mo
ther formation tad even come cle to Basal he com
soie chamber (or cavity) A the EM ration within
the cavity i mid aad absarbed by the walls of he eno
ue none ers trom outside This ensure hai spect
Komposition will math that emanating trom an ideal black
Sars the goal et pets the peche con
hat would emerge from a sal opening in th cavity Totaly
Symi by the problem. as a as resort, Planck red 1 the
asia aa analy is of Maxwell nd Bolan, which
vas developed as the bass ofthe inci theory of gases.
Pislosophicaly this isa completely éeteininic stent
‘hat ssumes one can follow, a leas principle, every stom
“sones around ia the system. Consequeny, cach tom it
taken to be recognizable independent and enumerabl, For
rely computational nus, Planck posada each
008 0 the selon ning the wall ofthe chamber cold
ahs and emi only see amounts of energy proportonal
toto frequency. These ener oli ere cual o
mile fh, re À now called Plane’
a Being arar
Constant, vas (und 1 be 6.626 = 10
traditional man, Planck otherwise held fatto te classical
‘ase piste of ight sisting that ony the oscilar were
quantized
Props. Thomson (1903) —thedncoerer othe
econ extended the ies. ges tha elecromagret
ace mg cale be aca afferent fom oer waves
perhaps local concentration el radiant energy uly existed
Thomson had observed tat when a beam of high-frequency
EMtadiation (X-rays) as shone onto a gs, only eran of
the atoms, bee and there, wer onze. Iwai the pam
Td hot spots ral than having its eco distrito con
rinousty overt aveo Gas photo at Tp of page 5):
The conset of the photon in ite modem incarnation eae
well known Inverse Square Law. which is easily vetted
‘il point source and à photographic exposure mete
3.3.3 Photons
Light sbsoehed and mid in ing dirt hart in par
cles of electromagnetic"Mull.” known x photons. That much
ts been confirmed ands well ewablshed, ut he question
‘of whether or os light is el” a stream of photons ae
frm ted it hat sue Wi be tevin vera Ges
Ordinaria light beam delivers many minute energy
ana at erent grrr natures oly hdc und à
Ésminoous phenomenon is observed macroscopically. That
Som of bin i commonplace in Nature e forces exerted by
(beindiidn gus molecules in a wind blend nto what sens
Sonia presore, butt obvogsy Indeed Bar nal
‘ogy beeen à gas and à Now of photons ise we will come
taco present
A AE great French lic LOU de Broglie pt
‘Light im sor hemos fined form of mate,” and all
mater, including light, fe quamzed. At base e comes in
minute elementary uni qurks,Ioptons, and photons, That
‘overarching un is among the most appealing encon 10
mac Ih photon as parco (whatever à "pail 1)
The Failure of Classical Theory
In 1900 Max Planck produced a rather etait, nd some
what eroneois, analysis ofa process Known as Mack
radiation p. SD. Nonetheless, the expression he same ap
‘ith betty al he exis experiment dat, fst mo
ther formation tad even come cle to Basal he com
soie chamber (or cavity) A the EM ration within
the cavity i mid aad absarbed by the walls of he eno
ue none ers trom outside This ensure hai spect
Komposition will math that emanating trom an ideal black
Sars the goal et pets the peche con
hat would emerge from a sal opening in th cavity Totaly
Symi by the problem. as a as resort, Planck red 1 the
asia aa analy is of Maxwell nd Bolan, which
vas developed as the bass ofthe inci theory of gases.
Pislosophicaly this isa completely éeteininic stent
‘hat ssumes one can follow, a leas principle, every stom
“sones around ia the system. Consequeny, cach tom it
taken to be recognizable independent and enumerabl, For
rely computational nus, Planck posada each
008 0 the selon ning the wall ofthe chamber cold
ahs and emi only see amounts of energy proportonal
toto frequency. These ener oli ere cual o
mile fh, re À now called Plane’
a Being arar
Constant, vas (und 1 be 6.626 = 10
traditional man, Planck otherwise held fatto te classical
‘ase piste of ight sisting that ony the oscilar were
quantized
Props. Thomson (1903) —thedncoerer othe
econ extended the ies. ges tha elecromagret
ace mg cale be aca afferent fom oer waves
perhaps local concentration el radiant energy uly existed
Thomson had observed tat when a beam of high-frequency
EMtadiation (X-rays) as shone onto a gs, only eran of
the atoms, bee and there, wer onze. Iwai the pam
Td hot spots ral than having its eco distrito con
rinousty overt aveo Gas photo at Tp of page 5):
The conset of the photon in ite modem incarnation eae
$2 Chapter 3 Ebchosapat Tey, Pie
{to being 1905 by way of Ein bilan orten
EM radiation, it emits leo, The deal of tat poses
ud been studied experimental fr decade, bu dled
analyse via clinical Eletomagetic Teo ini sta
tag ueament eased th the electromagnet field elf
the product of Planck's Constant and the frequency of he ih
son fil
Photons are table, charges, males lemandary parles
‘hate nly athe speed <
In 192 Sandra. Rove formulas a nv and
oof of Picks laAbody quon ain ical mods
pie gt quanto. Te ety was vince filed
Vik a us o photons, which were an o Be al ind
tingiehble, one fromthe cer. Tt was racial etre
wierpanice wer complet rchangsbl and tis had
3 proud loc on he scica formulation ira mate
rater casque que
‘ery oer parc and no a of ther can be ken asta
ndependent way Sal microparticles
feret rom the
beave nan orinar eas The quamin-meshanisalprobti
fy fortion a describes te inca beto of thermal
tm niert, became aire pri tol of theoreti
Une ordinary object, photons cannot Be seen dret:
hats ren of them comes from observing the rs of
hele beg eer erated or anne igh never sen
ja sling long through space. À photon I obierved y
cts the effet has un ls soundings and only a
sce Photo afi en ed o charge pales mar
enh ae mie fom and abs y lesions. And
am. A mumbo o experiment have desl ned the
ature ofthe emision proces or example, imsgine
piotdeecos cach capahl of menring mince amount u
‘wave, as is maintained clasícall, a the dewectors should re
Nr eschemie pus in oinedene. That doe mi happen,
instead, count ae ere hy detectors indeprderty, om
localized light quant random directions
mis ight ea pon) reci in he oppose ection
Sint apto rote when fits a alle, Pi, 3.20 tone
int narrow hea They soo spontanen, radiate photons
in random dictions and ar seals Kicked backward
{to being 1905 by way of Ein bilan orten
EM radiation, it emits leo, The deal of tat poses
ud been studied experimental fr decade, bu dled
analyse via clinical Eletomagetic Teo ini sta
tag ueament eased th the electromagnet field elf
the product of Planck's Constant and the frequency of he ih
son fil
Photons are table, charges, males lemandary parles
‘hate nly athe speed <
In 192 Sandra. Rove formulas a nv and
oof of Picks laAbody quon ain ical mods
pie gt quanto. Te ety was vince filed
Vik a us o photons, which were an o Be al ind
tingiehble, one fromthe cer. Tt was racial etre
wierpanice wer complet rchangsbl and tis had
3 proud loc on he scica formulation ira mate
rater casque que
‘ery oer parc and no a of ther can be ken asta
ndependent way Sal microparticles
feret rom the
beave nan orinar eas The quamin-meshanisalprobti
fy fortion a describes te inca beto of thermal
tm niert, became aire pri tol of theoreti
Une ordinary object, photons cannot Be seen dret:
hats ren of them comes from observing the rs of
hele beg eer erated or anne igh never sen
ja sling long through space. À photon I obierved y
cts the effet has un ls soundings and only a
sce Photo afi en ed o charge pales mar
enh ae mie fom and abs y lesions. And
am. A mumbo o experiment have desl ned the
ature ofthe emision proces or example, imsgine
piotdeecos cach capahl of menring mince amount u
‘wave, as is maintained clasícall, a the dewectors should re
Nr eschemie pus in oinedene. That doe mi happen,
instead, count ae ere hy detectors indeprderty, om
localized light quant random directions
mis ight ea pon) reci in he oppose ection
Sint apto rote when fits a alle, Pi, 3.20 tone
int narrow hea They soo spontanen, radiate photons
in random dictions and ar seals Kicked backward
ts baca quantum mechanical fc consistent wi he
usa pure of the emision of a symmeiical wave
A Barrage of Photons
nese numbers of pricians the we of statistical tech
be clasical MaxwllBolmn aie or ding
‘aise for idinguishble particles): Bose-Einstein and
de Paul Exclusion Péncpl de „panices that hae ero or
‘ue the Pat Exclusion Pac he ose war have
mens. they ar spin prices and te manner in which
thy group together obeys Bowe Fine sais. Shay.
‘ens ae fermion they ar pin paies that hey Fe
Micros have Genie PAT chart ich
‘When thse rive, we have completely specified he kind
Spuk being considered. Aleratvely there ar lee
opera of any given microparticle hat describe ts omen
I. When a these erie quien are given. we have
te momen
a ema des lc he
‘her Wien ese a
Sumter f phon oca he same se er tre
Try ofthe tba seta onthe one
‘apne fd appear asthe conénune median fan
‘ae (withthe sc enr. same een. sme morc
In San econ) Deren mone ane wees
rc aren a -
cf timate inte ae stan
Fora uniform monochromati ph ea of regen
QUIM Y A isthe vers ner pons mpeg
Sn aun rc normal he Pea) perunı time, name. he
‘hoon lx density. More realistically ih beam quan
impnochromaic 17) wi an erage regency, men
‘monochromatic Beam hs ross sectional re As mean
‘bere isthe optical per ofthe Bea in wa, The mean
Df time (Table 3.1). For example. small 1.0 mW He Ne
Toserbeam with a mean wavelngi of 328 am delivers a
‘ean photon fx of Ph, = (10% 10° Wy (6 526%
10 2398 x 1089 66328 % 10°" my) = 32 %
10° photons per second
Imagine a wndor beam of light having a conan mad
ane nd era can ean poor fyi os
‘cren, The energy ofthe beam le deposited an th screen ina.
‘ard May of minute burs Individual, he Incoming
photons register at locations onthe plane tat are totaly
Sapreditble, ad ante at moment in ime tht ace ely
‘predictable It looks a fihe bam is composed of aan
Steam of photons bl that conclusion, however ep,
nes beyond the bervton. Waa car bid eat ight
‘eter ite emery in a cat of impact that ar andor in
pace and ime actos the beam
‘Suppose thal we project lsh patte onto the ren: e
sight be a st of interference fringes or the image of à
Romans ace, The hare of photons forming the image
TABLE 3.1 The Mean Photon Flux Denaky for
a Sampling of Common Sources.
aie ican Pres Fux Dany
Source Ain nis poto md)
usa pure of the emision of a symmeiical wave
A Barrage of Photons
nese numbers of pricians the we of statistical tech
be clasical MaxwllBolmn aie or ding
‘aise for idinguishble particles): Bose-Einstein and
de Paul Exclusion Péncpl de „panices that hae ero or
‘ue the Pat Exclusion Pac he ose war have
mens. they ar spin prices and te manner in which
thy group together obeys Bowe Fine sais. Shay.
‘ens ae fermion they ar pin paies that hey Fe
Micros have Genie PAT chart ich
‘When thse rive, we have completely specified he kind
Spuk being considered. Aleratvely there ar lee
opera of any given microparticle hat describe ts omen
I. When a these erie quien are given. we have
te momen
a ema des lc he
‘her Wien ese a
Sumter f phon oca he same se er tre
Try ofthe tba seta onthe one
‘apne fd appear asthe conénune median fan
‘ae (withthe sc enr. same een. sme morc
In San econ) Deren mone ane wees
rc aren a -
cf timate inte ae stan
Fora uniform monochromati ph ea of regen
QUIM Y A isthe vers ner pons mpeg
Sn aun rc normal he Pea) perunı time, name. he
‘hoon lx density. More realistically ih beam quan
impnochromaic 17) wi an erage regency, men
‘monochromatic Beam hs ross sectional re As mean
‘bere isthe optical per ofthe Bea in wa, The mean
Df time (Table 3.1). For example. small 1.0 mW He Ne
Toserbeam with a mean wavelngi of 328 am delivers a
‘ean photon fx of Ph, = (10% 10° Wy (6 526%
10 2398 x 1089 66328 % 10°" my) = 32 %
10° photons per second
Imagine a wndor beam of light having a conan mad
ane nd era can ean poor fyi os
‘cren, The energy ofthe beam le deposited an th screen ina.
‘ard May of minute burs Individual, he Incoming
photons register at locations onthe plane tat are totaly
Sapreditble, ad ante at moment in ime tht ace ely
‘predictable It looks a fihe bam is composed of aan
Steam of photons bl that conclusion, however ep,
nes beyond the bervton. Waa car bid eat ight
‘eter ite emery in a cat of impact that ar andor in
pace and ime actos the beam
‘Suppose thal we project lsh patte onto the ren: e
sight be a st of interference fringes or the image of à
Romans ace, The hare of photons forming the image
TABLE 3.1 The Mean Photon Flux Denaky for
a Sampling of Common Sources.
aie ican Pres Fux Dany
Source Ain nis poto md)
any given location, But we can determine the kl o
sured (or classically computed) value ofthe irradiance is
proportional to he probably of detecting a photon at that
Teen p13.
photons, ne podived using a spec kind of pho
noose lise phone
nce (=I "in inc aie cysts ech opi
eng pan Ag tom One or mor sve
evelopment cemer on
Spa eh dep
igure 321 shows à series of photographs sen with
he expove pl, The fla
ing pe gos ep magyar 0 or ach se
Horn he image, he tal tre of he press fox
and he pare same a amir sonimows appesrance
Photon Counting
that question. sachen win the st 35 ear ave
Sande enperiment in wich they Wry counted id
af photons was care of he pe of source Wes
nso th hort dts here ot ts Informa a
sured (or classically computed) value ofthe irradiance is
proportional to he probably of detecting a photon at that
Teen p13.
photons, ne podived using a spec kind of pho
noose lise phone
nce (=I "in inc aie cysts ech opi
eng pan Ag tom One or mor sve
evelopment cemer on
Spa eh dep
igure 321 shows à series of photographs sen with
he expove pl, The fla
ing pe gos ep magyar 0 or ach se
Horn he image, he tal tre of he press fox
and he pare same a amir sonimows appesrance
Photon Counting
that question. sachen win the st 35 ear ave
Sande enperiment in wich they Wry counted id
af photons was care of he pe of source Wes
nso th hort dts here ot ts Informa a
(45, The Dean has pica wer bik
iron ne averaged nation om Ba OAD) a0
sponding mean patos lux @ F
‘dom aval of photons onan cl thi shor pare
sosúble forthe macroscopic quantity Pu he measured to be
sant, eventhough thee sm undetying discontinuous
‘Nov ps th barn through hon sha tye open fora
ring phototecor ding that neva Ar ri
sandy of is The resul are prescrie in aPstogram
(Fig 323), where the number of al in which N photons
ame
tonta 55
were sound is plotted against N. Few wa reger ciber
only approximates te wel-known Pan urn. 1
tral interval tasting a time F wil record ero photons, one.
hotm. no photons. ards oth,
The Poisson diatbuton i the same symmetrical curve
one gts when outing ir the number of parts rar
‘Somly emited by à long-ivedradiwcive sample. or Ihe
number of raindrops randomly descending on an aes na
Ste see Ts aa the UE O PIO of et
2 head, poned against the umber af heads occurring 1
fr a coin toed more than about 20 times, This with
Nino = 20 ie highest probailiy ers neo He
Y +20. The mox probable vale will he 10
eas amis small U would seem tha
“Meal ser produces igh generates 2 stream a phon
ea. Hor casos that wll explored lata al mone
‘etic beam menochromate plane wave
‘tbat is known as coherente
Nos ping, he stata isribucion ofthe number
ef photons arriving ata detector depends on the nature of he
ares fundamental different for an al coherent
rc alone Extreme as compares 10 an cally lized
À stabile laser resembles coberen source, and an or
ory thera
«ne mp more one} resembles a chao ours athe
me of ordinary light tte are inherent actus i the
invadianse and therefore nthe optical power (p48) These
Toons, hough random ini somespondingly a
related (Fig. 326), The reser the optical pow, te
Bree the number density of photons. ca the aval of
Photons a the detector e nota succession of independent
vent, BoseFitein static apply (Fg. 329) Her he
mos likely number of counts per Intrval zer, whereas
deity tor er igh mon key more of peo he
ter eeorded.Thuceven ia been of le ligt nd à beamof
‘rest that extents beyond clasica! ho.
iron ne averaged nation om Ba OAD) a0
sponding mean patos lux @ F
‘dom aval of photons onan cl thi shor pare
sosúble forthe macroscopic quantity Pu he measured to be
sant, eventhough thee sm undetying discontinuous
‘Nov ps th barn through hon sha tye open fora
ring phototecor ding that neva Ar ri
sandy of is The resul are prescrie in aPstogram
(Fig 323), where the number of al in which N photons
ame
tonta 55
were sound is plotted against N. Few wa reger ciber
only approximates te wel-known Pan urn. 1
tral interval tasting a time F wil record ero photons, one.
hotm. no photons. ards oth,
The Poisson diatbuton i the same symmetrical curve
one gts when outing ir the number of parts rar
‘Somly emited by à long-ivedradiwcive sample. or Ihe
number of raindrops randomly descending on an aes na
Ste see Ts aa the UE O PIO of et
2 head, poned against the umber af heads occurring 1
fr a coin toed more than about 20 times, This with
Nino = 20 ie highest probailiy ers neo He
Y +20. The mox probable vale will he 10
eas amis small U would seem tha
“Meal ser produces igh generates 2 stream a phon
ea. Hor casos that wll explored lata al mone
‘etic beam menochromate plane wave
‘tbat is known as coherente
Nos ping, he stata isribucion ofthe number
ef photons arriving ata detector depends on the nature of he
ares fundamental different for an al coherent
rc alone Extreme as compares 10 an cally lized
À stabile laser resembles coberen source, and an or
ory thera
«ne mp more one} resembles a chao ours athe
me of ordinary light tte are inherent actus i the
invadianse and therefore nthe optical power (p48) These
Toons, hough random ini somespondingly a
related (Fig. 326), The reser the optical pow, te
Bree the number density of photons. ca the aval of
Photons a the detector e nota succession of independent
vent, BoseFitein static apply (Fg. 329) Her he
mos likely number of counts per Intrval zer, whereas
deity tor er igh mon key more of peo he
ter eeorded.Thuceven ia been of le ligt nd à beamof
‘rest that extents beyond clasica! ho.
|
3.3.4 Radiation Pressure and Momentum
Feared mater Fora ile eme hough is fe
igh as sb he spent of he omc over
he wave theory, atl the experiment fort tht cd
jst by extablishingtheorciclly tht wanes d indeed exer
Are Maxwell, "here is a pressure in the direcion normal
crm oe flow of energy, sesame o expe ar
[At Massel showed the radialen pressure, gal be
Notice hr this equation has the unis f power divides by
re. divided hy speed. or equivalent, fore times speed
‘vided are and sped, ru force oer ar, ee
Instantancos prewure that would be exered on pert
1yabsorbing surface y a normaly incident bas
nach ath and Held re ly vaig. Se
api varying, st mint) pact deal with he
CAN
ca os
pe innen ge gare meer This une pee à
Referring back to Fi. 3.16. pis momentum, the force
3.3.4 Radiation Pressure and Momentum
Feared mater Fora ile eme hough is fe
igh as sb he spent of he omc over
he wave theory, atl the experiment fort tht cd
jst by extablishingtheorciclly tht wanes d indeed exer
Are Maxwell, "here is a pressure in the direcion normal
crm oe flow of energy, sesame o expe ar
[At Massel showed the radialen pressure, gal be
Notice hr this equation has the unis f power divides by
re. divided hy speed. or equivalent, fore times speed
‘vided are and sped, ru force oer ar, ee
Instantancos prewure that would be exered on pert
1yabsorbing surface y a normaly incident bas
nach ath and Held re ly vaig. Se
api varying, st mint) pact deal with he
CAN
ca os
pe innen ge gare meer This une pee à
Referring back to Fi. 3.16. pis momentum, the force
ce hye Ram on an bing sure
19-22 ix
Gar ech time ners an
ES
ap 4
Hence the volume demity of elestremapneie
a enced wih veloc wllemerge wilh
momar tht our on orion, and hc
Note. rom Egs 3.50) and 0.32).
tere wl ea corresponding momentum € ranspad po
ond
tre. ach quantum ar an energy € = he
‘Ween en expecta photon cary mamennun
ir acy with Special Relativity, which relate the mass
These quant sve Been confine
er and mamentum an 1. an lection up
"hic average fax desiy of elt
the Sun impinging normally on a surface jst 0
Fant’ molto in ba 1400 W m’. As
TA 10 Pounce em ax campus with
fhe Gai stn, ba isl sponsible fora subst
‘ofthe Sam rditio peste relatively amall ae Poble
3.3 Asone might exc, becomes sega within he
ing ty of ge hp sa. ber plays a ica
an in suppose str galos poy. Desp the Sus
elect over long acting men. Far eampe, ad the presse
een neglected it would have mined Mars y about 48 O.
rs of sunlight o propel a space vehicle among Ie ler
19-22 ix
Gar ech time ners an
ES
ap 4
Hence the volume demity of elestremapneie
a enced wih veloc wllemerge wilh
momar tht our on orion, and hc
Note. rom Egs 3.50) and 0.32).
tere wl ea corresponding momentum € ranspad po
ond
tre. ach quantum ar an energy € = he
‘Ween en expecta photon cary mamennun
ir acy with Special Relativity, which relate the mass
These quant sve Been confine
er and mamentum an 1. an lection up
"hic average fax desiy of elt
the Sun impinging normally on a surface jst 0
Fant’ molto in ba 1400 W m’. As
TA 10 Pounce em ax campus with
fhe Gai stn, ba isl sponsible fora subst
‘ofthe Sam rditio peste relatively amall ae Poble
3.3 Asone might exc, becomes sega within he
ing ty of ge hp sa. ber plays a ica
an in suppose str galos poy. Desp the Sus
elect over long acting men. Far eampe, ad the presse
een neglected it would have mined Mars y about 48 O.
rs of sunlight o propel a space vehicle among Ie ler
38 Chapter 3 Bonne Ta, rt we OW
“The peste exerted by light was actually mesure ss
coheed 185-191) an inept De
se Hal (70-140) Te compiten fomi
Aon oT erst prance init nr
o oA STS AE
bree o alan open sah sg Do.
OT UT CT es
are cs tat lb teed at (p30.
3.4 Radiation
Flsironingneti rn comes «Broad ange of wave
the sane pe. Despite he fact tat we distinguent
rmirowaves. inte. and a forth hte sony one ey
tone ewence ol electemagneic wave, Maxwells Equations
Are inéependent of wavelength an o suggest no fondamental
Senex kind. Accor era To ok or a
Fin that the various types of aan energy seem to have à
eon origin i ha they ate all asociaed wih noni
‘nthe clesromagnetic He, and changer har which ies se
A satin charge ha a constat Eels no El, and
tum if A uno moving charge has otha E and
"nem eed e ack athe reve as, amor
fo see at all if the charge stopped radiating just because you
and walking along next vo 1. Ta lentes nant
murine chen. which seared do dit In he photon pi
ares undersord bythe conviction thatthe funded
= Yee info ue ches Ghost ond vt
That mich ror charges changing spe ong ht
eyes or pp essing Fac and fn In a re
eg poser En een ee wr ai ed
treaty ver agora oi na Do
men specie ied
3.4.1 Linearly Accelerating Charges
Considera charge moving a a consta speed. e senal
les atached o a unchsuing rata elect field and sr
Space the E-ield changes om momen! to moment at amy
instant ite valu can be determined by supposing ta the eld
Tes moe along. Fed 1 the charg. Ths the eld docs not
lenge rom the hare, and there radiation
The elec ed ol char rt an De represented 8
Sines. For a charge moving al consta! velocity Y the field
Tine a il radial and tag. bu they ne no Longer en
ghspeed and usualy RME when ==
Fyre 22 Ech bl say son. Ei lt
“The peste exerted by light was actually mesure ss
coheed 185-191) an inept De
se Hal (70-140) Te compiten fomi
Aon oT erst prance init nr
o oA STS AE
bree o alan open sah sg Do.
OT UT CT es
are cs tat lb teed at (p30.
3.4 Radiation
Flsironingneti rn comes «Broad ange of wave
the sane pe. Despite he fact tat we distinguent
rmirowaves. inte. and a forth hte sony one ey
tone ewence ol electemagneic wave, Maxwells Equations
Are inéependent of wavelength an o suggest no fondamental
Senex kind. Accor era To ok or a
Fin that the various types of aan energy seem to have à
eon origin i ha they ate all asociaed wih noni
‘nthe clesromagnetic He, and changer har which ies se
A satin charge ha a constat Eels no El, and
tum if A uno moving charge has otha E and
"nem eed e ack athe reve as, amor
fo see at all if the charge stopped radiating just because you
and walking along next vo 1. Ta lentes nant
murine chen. which seared do dit In he photon pi
ares undersord bythe conviction thatthe funded
= Yee info ue ches Ghost ond vt
That mich ror charges changing spe ong ht
eyes or pp essing Fac and fn In a re
eg poser En een ee wr ai ed
treaty ver agora oi na Do
men specie ied
3.4.1 Linearly Accelerating Charges
Considera charge moving a a consta speed. e senal
les atached o a unchsuing rata elect field and sr
Space the E-ield changes om momen! to moment at amy
instant ite valu can be determined by supposing ta the eld
Tes moe along. Fed 1 the charg. Ths the eld docs not
lenge rom the hare, and there radiation
The elec ed ol char rt an De represented 8
Sines. For a charge moving al consta! velocity Y the field
Tine a il radial and tag. bu they ne no Longer en
ghspeed and usualy RME when ==
Fyre 22 Ech bl say son. Ei lt
Fire 327 Gace Flo vty crane once
ln contrast Fig. 3.27 shows th fl fines associated with
a leon ace rai uniform tothe right. The points O,
‘Os Ou amé O, are the positions ofthe electron after equal
i ineral The eld Ins ae now curved, and bis as
scant ference. Asa Furr cont, Fig. 328 depicts he
of an electron at sore array tne Before t= Othe
ice was always testa the point O The charge was then
«nori accelerated until me racing. a sped which
‘as ainaied constant hreier We an anticipate hs the
Sumounding feld ies will somehow ear the information
tht de electro has accelerated. We have ample reason o
sue that is “information wil prpagate a he sped
no pit beyond 3 m from ©
I or example, = 10"
oul e aware ofthe fact hate char had even moved
Ale ines in that region would be uniform, sisi, and
tee on O, a if the charge were sil there Attimo 1 the
son it point Os moving witha constant speed Inthe
ii of Os he fi ines must then sesembl those 0 Fi
324%. Gauss s Law requires thatthe lts ouside the sphere
rad sont those within the phere of adas ls =
sine there ae no charge between them. Ie now app
24 nai so
tht rng te intra when the partic alee, the
Gel ines became distorted and a ak appeared THe ka
ape othe nes withthe repo of he Kink o ter
thor. Wha significant sha there now eit man
verse component ofthe electro field E. which propagates
tar a pulse. At some point in pac the tranmien ee
accompanied by a magnetic ld
The ati component ofthe lc ed drops off as 1/7
while de wansverecomposeatgoesas rage distances
frome ee en ee, om
©, te eects
Fora postive charge moving slowly (o
and magnetic radiation els canbe shown tbe propor
{oF (Fa) and XP) respectively, where dis the el
ton Fora negli charge e revere oscars, a6 sown
figure 328 Anne Era oes
“toe dat ans cocina 2 Trans metas o
ln contrast Fig. 3.27 shows th fl fines associated with
a leon ace rai uniform tothe right. The points O,
‘Os Ou amé O, are the positions ofthe electron after equal
i ineral The eld Ins ae now curved, and bis as
scant ference. Asa Furr cont, Fig. 328 depicts he
of an electron at sore array tne Before t= Othe
ice was always testa the point O The charge was then
«nori accelerated until me racing. a sped which
‘as ainaied constant hreier We an anticipate hs the
Sumounding feld ies will somehow ear the information
tht de electro has accelerated. We have ample reason o
sue that is “information wil prpagate a he sped
no pit beyond 3 m from ©
I or example, = 10"
oul e aware ofthe fact hate char had even moved
Ale ines in that region would be uniform, sisi, and
tee on O, a if the charge were sil there Attimo 1 the
son it point Os moving witha constant speed Inthe
ii of Os he fi ines must then sesembl those 0 Fi
324%. Gauss s Law requires thatthe lts ouside the sphere
rad sont those within the phere of adas ls =
sine there ae no charge between them. Ie now app
24 nai so
tht rng te intra when the partic alee, the
Gel ines became distorted and a ak appeared THe ka
ape othe nes withthe repo of he Kink o ter
thor. Wha significant sha there now eit man
verse component ofthe electro field E. which propagates
tar a pulse. At some point in pac the tranmien ee
accompanied by a magnetic ld
The ati component ofthe lc ed drops off as 1/7
while de wansverecomposeatgoesas rage distances
frome ee en ee, om
©, te eects
Fora postive charge moving slowly (o
and magnetic radiation els canbe shown tbe propor
{oF (Fa) and XP) respectively, where dis the el
ton Fora negli charge e revere oscars, a6 sown
figure 328 Anne Era oes
“toe dat ans cocina 2 Trans metas o
x
>
Has
A
sí I~
x
«Fr
A
rene era mem
Energy is mont rang radiated perpendicular tthe ae
Tc energy tht radin out no the smounding space
responsible frie wceleraing Free, which in tum does work
me charge
3.4.2 Synchrotron Radiation
A ie charg gic usen an ay sor of curved ah
wil rado, This provides perl mech
tlle 170 fos ha Comps ef caged
‘ely car un rc amd sed The
sft cain whch coma ga amon) and
‘charged particle slowly nvolving in a ira bit a
te à douse shaped pate simile o tb ne epicte in
Fig. 3.29. Again the sation of ai de symmeticl
around & which i sow the cenital acceleration acting
inward lng he adi dean from cet ofthe cul
II the shige. And. once mote emery i mot ro
‘radiated perpendeutar o sh acceleration causing e tie
higher the seed the cea rer et the ot
hie he forward ode late the dicton of motion. At
ape aproxime < the patil beam aly with à dam
tor comparable to tha of à Straight pin) radiates essentially
Song ou one poiting angen othe obi he nta
anexas direction of ¥ (Fig 3.30). Moreover, [or y = the
radiation willbe songs polarze ine plane ofthe motion
This "searchlight offen less thon a Tew millimeters in
ameter, <wecps around asthe parle clumps cicle the
‘machine, much ike the headlight om 3 rin rounding tm
Wi cach revolution the beans momentarily (< 05 ashes
Up. when gra has shor dation mos comprise à
Intense source of rapidly pulsating radiation tunable over a
wide range of feequeies, fom Infrare 1 Hight 0 Xray
Fire 220 Runen sn er one
>
Has
A
sí I~
x
«Fr
A
rene era mem
Energy is mont rang radiated perpendicular tthe ae
Tc energy tht radin out no the smounding space
responsible frie wceleraing Free, which in tum does work
me charge
3.4.2 Synchrotron Radiation
A ie charg gic usen an ay sor of curved ah
wil rado, This provides perl mech
tlle 170 fos ha Comps ef caged
‘ely car un rc amd sed The
sft cain whch coma ga amon) and
‘charged particle slowly nvolving in a ira bit a
te à douse shaped pate simile o tb ne epicte in
Fig. 3.29. Again the sation of ai de symmeticl
around & which i sow the cenital acceleration acting
inward lng he adi dean from cet ofthe cul
II the shige. And. once mote emery i mot ro
‘radiated perpendeutar o sh acceleration causing e tie
higher the seed the cea rer et the ot
hie he forward ode late the dicton of motion. At
ape aproxime < the patil beam aly with à dam
tor comparable to tha of à Straight pin) radiates essentially
Song ou one poiting angen othe obi he nta
anexas direction of ¥ (Fig 3.30). Moreover, [or y = the
radiation willbe songs polarze ine plane ofthe motion
This "searchlight offen less thon a Tew millimeters in
ameter, <wecps around asthe parle clumps cicle the
‘machine, much ike the headlight om 3 rin rounding tm
Wi cach revolution the beans momentarily (< 05 ashes
Up. when gra has shor dation mos comprise à
Intense source of rapidly pulsating radiation tunable over a
wide range of feequeies, fom Infrare 1 Hight 0 Xray
Fire 220 Runen sn er one
When masts we make the cicubtingstsrons wig. hu Fingered hoe trough a mb end plat
These ae eide a is four ghaograghs, which were
He voor ea each picture Since mn on
rada de eme is polanied in the oral plans
This belived tha majority of the low-fequeney
tates reaching the Ea rom one space have Wei
Eis
3.4.3 Electric Dipole Radiation
evap the sien clestomagnetic wave ordain mec
‘And yet his arrangement i surely the most important o all.
Both ph and lavo radiation ie primal rom
reamangementf the outros, or weakly bond, cons in
ons nd meets fellows (om De quantum mechanical
selpsis hat the lee dipole moment of the atoms the
major sure of is ain. The oe of ergy emission
shea : 2 schematically
iromagaetc waves. Figure 3.32
‘qua stationary positive hago. 1
Son. the lime dépendent
pole moment Ch asthe sali
+
Note mat At) could represent
de coles. momen of de
cian charge dition o
AU = 0.4 m = gd where d
‘moment i actully a vector in he
lei fom 4.0 +4. The fi
te shows a sequence of el Inc
aller as be displacement, and
meer 059
finaly revere direction. When
p= 0, sd the Held line mus
He voor ea each picture Since mn on
rada de eme is polanied in the oral plans
This belived tha majority of the low-fequeney
tates reaching the Ea rom one space have Wei
Eis
3.4.3 Electric Dipole Radiation
evap the sien clestomagnetic wave ordain mec
‘And yet his arrangement i surely the most important o all.
Both ph and lavo radiation ie primal rom
reamangementf the outros, or weakly bond, cons in
ons nd meets fellows (om De quantum mechanical
selpsis hat the lee dipole moment of the atoms the
major sure of is ain. The oe of ergy emission
shea : 2 schematically
iromagaetc waves. Figure 3.32
‘qua stationary positive hago. 1
Son. the lime dépendent
pole moment Ch asthe sali
+
Note mat At) could represent
de coles. momen of de
cian charge dition o
AU = 0.4 m = gd where d
‘moment i actully a vector in he
lei fom 4.0 +4. The fi
te shows a sequence of el Inc
aller as be displacement, and
meer 059
finaly revere direction. When
p= 0, sd the Held line mus
tre dipole, A it farther ou, in the region whee the conc
men shows that the elec fiel is composed is inet
terms and things ar sly complicated. Far rom the dipole,
in bai called he wave marion one he et cont
vaio is mac simples ha zone. a eed wavslength as
te established: and Bar arsscne, mula perpen,
ar, andi phase, Specially
BEE sn 8 cos br o
£ as
se = Br whee he il a oem asin Fi: 3.33. Te
Poyning vector = EC js alias point rally ont
sardine wave zone There. he il ne ar ile con
‘ti with and in plane prpendiular to, the dial ani
The iadance (rained edil onward from the sour)
an an iaverse-squute law dependence on distance, The
ans Mux density distribution à trois, ax in Fi, 329.
ty aki ofthe radiation patter, Notice the dependence of
heran, Tat (nu sl imponan when on
Rex not dic to ach an AC generator beson two
apa down that "wansmiting ancana "Figure 331 shows
= >
4 E
the arrangement amd to is Iogkal conclusion fly
mou efiienty Ht length comesponds o valen
‘save isthe formed atthe dio a syctonizaton wah te
cg curs producing AM af ave ae ur
Fey seal hundred meien eng. Consequen y the nes
ras in eue hs a pese red
{nthe ri, Tat at least saves some height allein the
dec o heal ly a. Mover, is eof he Eh
sen 25 and 100 me “
here most poopie with ado
3.4.4 The Emission of Light from Atoms
ua emision und bean of ada cry poca of
men shows that the elec fiel is composed is inet
terms and things ar sly complicated. Far rom the dipole,
in bai called he wave marion one he et cont
vaio is mac simples ha zone. a eed wavslength as
te established: and Bar arsscne, mula perpen,
ar, andi phase, Specially
BEE sn 8 cos br o
£ as
se = Br whee he il a oem asin Fi: 3.33. Te
Poyning vector = EC js alias point rally ont
sardine wave zone There. he il ne ar ile con
‘ti with and in plane prpendiular to, the dial ani
The iadance (rained edil onward from the sour)
an an iaverse-squute law dependence on distance, The
ans Mux density distribution à trois, ax in Fi, 329.
ty aki ofthe radiation patter, Notice the dependence of
heran, Tat (nu sl imponan when on
Rex not dic to ach an AC generator beson two
apa down that "wansmiting ancana "Figure 331 shows
= >
4 E
the arrangement amd to is Iogkal conclusion fly
mou efiienty Ht length comesponds o valen
‘save isthe formed atthe dio a syctonizaton wah te
cg curs producing AM af ave ae ur
Fey seal hundred meien eng. Consequen y the nes
ras in eue hs a pese red
{nthe ri, Tat at least saves some height allein the
dec o heal ly a. Mover, is eof he Eh
sen 25 and 100 me “
here most poopie with ado
3.4.4 The Emission of Light from Atoms
ua emision und bean of ada cry poca of
Thess minute negative pies, whic round heure
aise min of east, come kind of em en
icon The remainer fh oud soda od ino
lose," serial unresponsive. shel aroun and ig
und othe miles, Thee coed fl halls are made up
nes, we do kno with some crn tha ets mi ur
efectos lod, The mechanian k lm he predomi,
‘Usually an atom exis wiht chichofelecrom amunged
in some tbl onguation tat conespond 1 their ones
nergy ditbaion or eel: Every loto ii he lowes
Ip remain infil fet nse, Any mechan hat
pmp energy io the atm wl ler the ground sate For
Intact colision with anothers sn cion or ho.
On cam ater the ator energy sae Frans. Arto
a ent with teleton cous in rly cern spe on
figurations cemeponding to only sa vale ol neg In
tons occupier level higher ar route ech
the stom isi be exes conn hat inherey
promise higher temperatur, mean mor of he
Ss become ecited through tom solis. Ths sort of
mechanism indicate of clas frech gent excita
tione—zlow dscarge Mame, spark and x or ich
eh. and the meaty
fred nd uel
‘When enough energy imparted oan tom (pal
ig. 3.35, Th elton vil make a very rapid ration. à
‘quantum ump, rom te ground-state oral onu o
ie ofthe well linen exited ae, oe of he quand
fangs on is energy adder. Axel. hr amount of er
ken pin he proces equal the nergy diference beeen
‘he nina and fina sates, and since vat spec and elt
define ine amount of energy Mar can be absorbed B an
Usa fer abou 10 1001 10 te ented som spr
tare relies hack lower sae, most fe he round
sing te nain eal a. Th ee
Songe It chi ru dan
nos of he norton ite word rod)
Be (ais ina ce o) energy he photon eset.
Ir meses he quantised ener deere of th tom Tt
Corresponds aspen requecy byway of = hate
aise min of east, come kind of em en
icon The remainer fh oud soda od ino
lose," serial unresponsive. shel aroun and ig
und othe miles, Thee coed fl halls are made up
nes, we do kno with some crn tha ets mi ur
efectos lod, The mechanian k lm he predomi,
‘Usually an atom exis wiht chichofelecrom amunged
in some tbl onguation tat conespond 1 their ones
nergy ditbaion or eel: Every loto ii he lowes
Ip remain infil fet nse, Any mechan hat
pmp energy io the atm wl ler the ground sate For
Intact colision with anothers sn cion or ho.
On cam ater the ator energy sae Frans. Arto
a ent with teleton cous in rly cern spe on
figurations cemeponding to only sa vale ol neg In
tons occupier level higher ar route ech
the stom isi be exes conn hat inherey
promise higher temperatur, mean mor of he
Ss become ecited through tom solis. Ths sort of
mechanism indicate of clas frech gent excita
tione—zlow dscarge Mame, spark and x or ich
eh. and the meaty
fred nd uel
‘When enough energy imparted oan tom (pal
ig. 3.35, Th elton vil make a very rapid ration. à
‘quantum ump, rom te ground-state oral onu o
ie ofthe well linen exited ae, oe of he quand
fangs on is energy adder. Axel. hr amount of er
ken pin he proces equal the nergy diference beeen
‘he nina and fina sates, and since vat spec and elt
define ine amount of energy Mar can be absorbed B an
Usa fer abou 10 1001 10 te ented som spr
tare relies hack lower sae, most fe he round
sing te nain eal a. Th ee
Songe It chi ru dan
nos of he norton ite word rod)
Be (ais ina ce o) energy he photon eset.
Ir meses he quantised ener deere of th tom Tt
Corresponds aspen requecy byway of = hate
‘mance frequency. neo several (ach With is wn kei
fod of cum) a wich te tom very etc sore
demi energy. The tom raie a quantum of energy that
ing econ
sl co some making is dowaward ence) tans
don vi gradually damped oscilory motion a the specific
romance frequency, The radiated light an tbn be env
Sei ma semiclascal way av ema in oros
Srestional ole, or wavetran, sing ls than oughly 105
‘a pictore that is im aproement with certain experimenta!
servations (se Section 7,42, and Fig. 7.36) f= useful 0
‘nko ths clctromagneti pulse a asnciaed in some inex
scale fasion withthe photon Ina way. he pue a se
clasica representation of he manifest ware nate ofthe
‘ton. Bu he io are equivalent inal spect: the le
tromagnetic wavctrin sa lasial ration tha describes the
Propagation ane pail dirivtion of ight extremely ei
Seti ener not quanired, and that isan ewe charac
ttc fte photon, So when we conside photon wave,
ep in nnd a there sore wo the ida than jot lei
iltory pulse of elestomagnetis wave. Of cous. thera
“an vent todo the notion ofthe emission of waves
‘lo have a sis fo aking about he Frequency of he eh
Tepes cta probe io y rive proton mod
lo What agency manifests the frequency
“The emission secta o ingle ators or low-pressure gas
Lane stos do nat me appre, cono = ar
ics tha fay well-defined reqencies characterise
ofthe atoms, There salvas some requeney broadening of
radio ie 10 some mation, colin, an 0 for
he tome ration fom one level to ano characte
Dea dy the emission of a well-defined, arrow range of
frequencies. On the the and, the spec of slid aná lg
nde aed ino wide frequency bands. When two atome are
respective energy levels became they act on each other. The
such sifted levis, in effet spreading out each oftheir
iin leves, blurring them into essentially conindous
hands Matra of this mate ei and absorb oer ad
range of roquencies
Optical Cooling
“Te incur momentum caiedby holon cane rusted
modo AÑ about ten tard absorption nd subequent
mission je, an om. which ee onginaly moving apor
haps 70 m/s, can he slowed to nar or send Since.in pen
al. erpeanr proportional to the average kin ners
AK) of the particles coming a system, thie process
‘alle’ apical or laser cooling. Wiki KE temperatures fn
become De bass fora variety of application including the
omic clock, the or interferometer, and the focusing of
om bes, For us rings together the iets ol Sections
334 and Sina competing practical way
Figure 3.36 depicts a beam of atom«, ach of mac mv
‘Flier photons having a propagación vector ky The ler re
‘quency rs selected be st neath the exon Freeh
{ 0m) ofthe atoms, Becase of ts motion. any prier
Popper shied upward by an amount 16,
‘When the laser frequency is tuned so hat = Pl + 0/0,
proces sch photon transfers its momentum of Ak 1
Shsrbing ato (6 p57) whose speed I ioreupan reduced
boy an amenas Bo She 130» M,
Fore 136. à mn one coh wh ts
e ar ee
fod of cum) a wich te tom very etc sore
demi energy. The tom raie a quantum of energy that
ing econ
sl co some making is dowaward ence) tans
don vi gradually damped oscilory motion a the specific
romance frequency, The radiated light an tbn be env
Sei ma semiclascal way av ema in oros
Srestional ole, or wavetran, sing ls than oughly 105
‘a pictore that is im aproement with certain experimenta!
servations (se Section 7,42, and Fig. 7.36) f= useful 0
‘nko ths clctromagneti pulse a asnciaed in some inex
scale fasion withthe photon Ina way. he pue a se
clasica representation of he manifest ware nate ofthe
‘ton. Bu he io are equivalent inal spect: the le
tromagnetic wavctrin sa lasial ration tha describes the
Propagation ane pail dirivtion of ight extremely ei
Seti ener not quanired, and that isan ewe charac
ttc fte photon, So when we conside photon wave,
ep in nnd a there sore wo the ida than jot lei
iltory pulse of elestomagnetis wave. Of cous. thera
“an vent todo the notion ofthe emission of waves
‘lo have a sis fo aking about he Frequency of he eh
Tepes cta probe io y rive proton mod
lo What agency manifests the frequency
“The emission secta o ingle ators or low-pressure gas
Lane stos do nat me appre, cono = ar
ics tha fay well-defined reqencies characterise
ofthe atoms, There salvas some requeney broadening of
radio ie 10 some mation, colin, an 0 for
he tome ration fom one level to ano characte
Dea dy the emission of a well-defined, arrow range of
frequencies. On the the and, the spec of slid aná lg
nde aed ino wide frequency bands. When two atome are
respective energy levels became they act on each other. The
such sifted levis, in effet spreading out each oftheir
iin leves, blurring them into essentially conindous
hands Matra of this mate ei and absorb oer ad
range of roquencies
Optical Cooling
“Te incur momentum caiedby holon cane rusted
modo AÑ about ten tard absorption nd subequent
mission je, an om. which ee onginaly moving apor
haps 70 m/s, can he slowed to nar or send Since.in pen
al. erpeanr proportional to the average kin ners
AK) of the particles coming a system, thie process
‘alle’ apical or laser cooling. Wiki KE temperatures fn
become De bass fora variety of application including the
omic clock, the or interferometer, and the focusing of
om bes, For us rings together the iets ol Sections
334 and Sina competing practical way
Figure 3.36 depicts a beam of atom«, ach of mac mv
‘Flier photons having a propagación vector ky The ler re
‘quency rs selected be st neath the exon Freeh
{ 0m) ofthe atoms, Becase of ts motion. any prier
Popper shied upward by an amount 16,
‘When the laser frequency is tuned so hat = Pl + 0/0,
proces sch photon transfers its momentum of Ak 1
Shsrbing ato (6 p57) whose speed I ioreupan reduced
boy an amenas Bo She 130» M,
Fore 136. à mn one coh wh ts
e ar ee
66 Copter Sucre hey Pas
By coat, an ion moving I he oppo des,
Note iat he ation presu force frequency depen
ed ie ia expec aed epee Tor vs
Doppler ict. That ans that, nd, bane 1 be pci
ery clever way thie accomplish
3.5 Light in Bulk Matter
Ths espe of dicks mi rocks
muss, be dealing with transparent dielectrics inthe for.
ar
Ths wer fect oF necia a on
zi io region of re space 1 hans a
Wa ass
Te tio ofthe ps ofan tronc wa In vacua
ii sn
‘ofthe medium.
VE va
agi substanse ht re unseren in he
wae apna the pect But we an
paa ante
{bland these ae sl esca “nonmagnetic” indeed, Ky
in 10° eg or diamond Ku = 1 = 22 1075, Setting
hoc presamad be
ndice in Tabl 321 relato seems to work well
on for some simple gave. The diff ares besan Ky
ad here wae actly remuencrdependen
dence ot n on te wavelength (or colo) oF Kie ia wel
ow so slld dispersion ares on a microscopio
Hess Newton se pri o dsprs white Reno it con
1 ant weil understand, eve Met
fon was well Know
TABLE 3.2. Maxwell's Relation
Gasca ad am
Subunce ”
ñ
Sate ”
Sold ton temperature
sumac VE 2
By coat, an ion moving I he oppo des,
Note iat he ation presu force frequency depen
ed ie ia expec aed epee Tor vs
Doppler ict. That ans that, nd, bane 1 be pci
ery clever way thie accomplish
3.5 Light in Bulk Matter
Ths espe of dicks mi rocks
muss, be dealing with transparent dielectrics inthe for.
ar
Ths wer fect oF necia a on
zi io region of re space 1 hans a
Wa ass
Te tio ofthe ps ofan tronc wa In vacua
ii sn
‘ofthe medium.
VE va
agi substanse ht re unseren in he
wae apna the pect But we an
paa ante
{bland these ae sl esca “nonmagnetic” indeed, Ky
in 10° eg or diamond Ku = 1 = 22 1075, Setting
hoc presamad be
ndice in Tabl 321 relato seems to work well
on for some simple gave. The diff ares besan Ky
ad here wae actly remuencrdependen
dence ot n on te wavelength (or colo) oF Kie ia wel
ow so slld dispersion ares on a microscopio
Hess Newton se pri o dsprs white Reno it con
1 ant weil understand, eve Met
fon was well Know
TABLE 3.2. Maxwell's Relation
Gasca ad am
Subunce ”
ñ
Sate ”
Sold ton temperature
sumac VE 2
Scattering and Absorption
Ware the pia BASTONES RENE OF
ation ofan adn coman wae with the ray
tosnvoming igh in two diffrent ways depending on the ii
i Govea the at will cetro Hg red
mi cape af ei
ply bot
rece the taking up ofa photon and its conversion it ber
ral energy) wa tone time widely Know a absorption,
raking op spot regudss of what hen happens othe
tive absorption. AN aerial sedis partake in dispo
In orar this exten process. ground sue oF 0
ICs ven ely ati nergy
Aa cr han th resonance eh
‘zation to any ofthe higher excited sates, Desp hat, he
regnet hi o! hs bites be supp 0 ine the
pin remain nus ground wae while fe load
her genes
pest tthe
aed so presurably wl oneal Dep To ad a hat
elastin ees. the atom resembles le dipole oscilla
And Mavwel Trey in a al way. 1 e soc
dos ste in dom dr —
ton and
35 Lena 67
spa oF 1 ph
condition in which he ators of lowepessie go ar or
Samy ening and Bin eee oscura modes abe
eons iting out photon tae of 100 rion per cond,
Genera, cm rane ia med ete be
an diary bea fight ic am behaves gh a
a "source" 1 à wemendaus number of photon (tes
Siam ol energy like this resembles classical spherical
wae: Thi we epi an om (ren thong i ple
do de so) at point source of spherical lecromane
outgoing ration inthe form of spherial wives does not
Wem a material with mo resonance in the visible is
cthed zh nonresonant scanering occurs andi gives
each participating atom the appearance of Beng ny
snurce af spherical wavelets, x lc, he ons the fe
‘quency ofthe incident hea toate romance, te
nthe vl be dsipativly absorbed Ms pe
‘hat crates sh ofthe vst appearance
many responsible fr he color ef your he
ine. the or fes and apples nd psn
35.1 Dispersion
Ixpersion correspond athe phenomenon whereby the
Inder of refraction ola medium frequency dependent
represen hs clar and magnets responses to applied E
And B el in terms of constants, and y Consequent. K
dependent of teqoency To dal heorcticaly with disper
Sion. is necessary 10 incorporate he atomic nate Prat
Ware the pia BASTONES RENE OF
ation ofan adn coman wae with the ray
tosnvoming igh in two diffrent ways depending on the ii
i Govea the at will cetro Hg red
mi cape af ei
ply bot
rece the taking up ofa photon and its conversion it ber
ral energy) wa tone time widely Know a absorption,
raking op spot regudss of what hen happens othe
tive absorption. AN aerial sedis partake in dispo
In orar this exten process. ground sue oF 0
ICs ven ely ati nergy
Aa cr han th resonance eh
‘zation to any ofthe higher excited sates, Desp hat, he
regnet hi o! hs bites be supp 0 ine the
pin remain nus ground wae while fe load
her genes
pest tthe
aed so presurably wl oneal Dep To ad a hat
elastin ees. the atom resembles le dipole oscilla
And Mavwel Trey in a al way. 1 e soc
dos ste in dom dr —
ton and
35 Lena 67
spa oF 1 ph
condition in which he ators of lowepessie go ar or
Samy ening and Bin eee oscura modes abe
eons iting out photon tae of 100 rion per cond,
Genera, cm rane ia med ete be
an diary bea fight ic am behaves gh a
a "source" 1 à wemendaus number of photon (tes
Siam ol energy like this resembles classical spherical
wae: Thi we epi an om (ren thong i ple
do de so) at point source of spherical lecromane
outgoing ration inthe form of spherial wives does not
Wem a material with mo resonance in the visible is
cthed zh nonresonant scanering occurs andi gives
each participating atom the appearance of Beng ny
snurce af spherical wavelets, x lc, he ons the fe
‘quency ofthe incident hea toate romance, te
nthe vl be dsipativly absorbed Ms pe
‘hat crates sh ofthe vst appearance
many responsible fr he color ef your he
ine. the or fes and apples nd psn
35.1 Dispersion
Ixpersion correspond athe phenomenon whereby the
Inder of refraction ola medium frequency dependent
represen hs clar and magnets responses to applied E
And B el in terms of constants, and y Consequent. K
dependent of teqoency To dal heorcticaly with disper
Sion. is necessary 10 incorporate he atomic nate Prat
ths ital charge tb i dione, This eomesponde
o he geasiaton of lee dipole rca, which I um
conta 1 he tot intemal We More simply stated the
Extemat fled separate postive and negative Charge in
medium (eck pir of which iva dipole), und these charges
then contribute an aditiona cd component he resina
tole moment per uni volume called the electric polar
Hration. P For most atria Band E are propoionl aná
cam sai Be ented hy
“Te relitiburion of hare and he consequent polation
cam occur ia te following nechanisme ere are molecule
Tat havea permanent dipole moment av ea of unequal
Sharing of valence electrons Ihe ae known as par me
ende; th oninar water mece a fay typical example
(Fig 337, Fach hydrogen onygen ond spar covalent.
‘wth he Heed pantie with respect othe Oc, Terma
again kepsthe molecular dipotesrandomiyoriemed. With
‘he intrdacton an este Held, ib dipoles ai then
selves, andthe dis aks on an orientational plaza
ton Inca of nomas tte and om, pp
¡cl ions he let sto, aufn I vetive the
cles thereby producing dipole moment In addition to
{his electron polarization, es is another process thats
‘sal NAC In he presence of un elect eld the positive
Dipole moment are therefore induced, resulting in what
Te he dels subjected an ack
omar wave wera care trace willespeienes
fie-varying fees andor teres These wil be proportion
re polar dieleciies. the molecules actual undergo rapid
miecue are itive lage and have apreciable moment
fine At high diving freuences polar molecles wll
Be ule o follow te Fld aeration. Tir contains
A6 wi dovrese and ill drop markelly The rat
secas of war's fay conse poro ima 0, p
AS
In cont lcrons have lite ie and an contin to
follow the eld conato) even at optical frequen
‘es to bout 5% 10° HT the dependence af non us
need by the interplay ofthe varios else polarization
in mind. is pose to drive an analytical expression for
sen yan ace ler fr ht ssi tin som
more about he details of al che internal atomic interactions.
o he geasiaton of lee dipole rca, which I um
conta 1 he tot intemal We More simply stated the
Extemat fled separate postive and negative Charge in
medium (eck pir of which iva dipole), und these charges
then contribute an aditiona cd component he resina
tole moment per uni volume called the electric polar
Hration. P For most atria Band E are propoionl aná
cam sai Be ented hy
“Te relitiburion of hare and he consequent polation
cam occur ia te following nechanisme ere are molecule
Tat havea permanent dipole moment av ea of unequal
Sharing of valence electrons Ihe ae known as par me
ende; th oninar water mece a fay typical example
(Fig 337, Fach hydrogen onygen ond spar covalent.
‘wth he Heed pantie with respect othe Oc, Terma
again kepsthe molecular dipotesrandomiyoriemed. With
‘he intrdacton an este Held, ib dipoles ai then
selves, andthe dis aks on an orientational plaza
ton Inca of nomas tte and om, pp
¡cl ions he let sto, aufn I vetive the
cles thereby producing dipole moment In addition to
{his electron polarization, es is another process thats
‘sal NAC In he presence of un elect eld the positive
Dipole moment are therefore induced, resulting in what
Te he dels subjected an ack
omar wave wera care trace willespeienes
fie-varying fees andor teres These wil be proportion
re polar dieleciies. the molecules actual undergo rapid
miecue are itive lage and have apreciable moment
fine At high diving freuences polar molecles wll
Be ule o follow te Fld aeration. Tir contains
A6 wi dovrese and ill drop markelly The rat
secas of war's fay conse poro ima 0, p
AS
In cont lcrons have lite ie and an contin to
follow the eld conato) even at optical frequen
‘es to bout 5% 10° HT the dependence af non us
need by the interplay ofthe varios else polarization
in mind. is pose to drive an analytical expression for
sen yan ace ler fr ht ssi tin som
more about he details of al che internal atomic interactions.
ic ae not totally disrupted hy small perturbation a net
Fore, F, mus exist that returns the system tn gum,
Moreover, we cn reasonably expect ha for very small ie
placement fon gala (where F = De force wil
Beiinar ia note words, poro! Fa) versus wil ct
he ais atthe eli point (x = 0) and wil Be à
tight ine ver close on eher side, Ths for small displace
maison be suposed hat the restoring force has he form
FS 2h 2, whore isa kind of cale constant much ike a
String consent Once somehow momentarily disturbed, an
sion bound inthis way wil osito aboutit equ
Psion with a natura or resonant frequency Bien by
85 = Vii Jn, tere its mass. This the osito
fequeny of the rien stem
A material median is envisined as anascmblags in vac
nm. of very ret many polacizablesloms each of which ie
nai by comparo io ie wavelength oiga) and close o
is ncighboı. When a ighmane implag on nich a medium.
ach tom can be thought a a a client forced osea
Being driven by the time-varying cis field Et) ol e
sav, which is assumed here be api in edicion
Fie 330 à à mean repre fo sch an
shell fastened 10 a iatonary postive muele by Mental
Springs Even under the llaminaion of Bright sunlight, the
empitude ofthe oscillations wil be no reser than about
10" m The forse, )exeredom an electron carge y by
the Eifel ofa harmonie wave of freauency a bofıhe form
FEIN = ap Ecos an
face sin Ihe opposite direction, whic is why ha minos
sign Newton's Second Law provides the equation of moto
dan se som of the freee equals the man res the ach
acht 36H)
The Fr erm on the elt ste sing force, and second is
the opposing restoring Cee. Toasty his expression wi
Tv fo Bea fuctis whose sondere Very much
‘Steen fom elf Funhermon, we cu cpt ae
ern wi ie athe some MSA an Hr KO
35 pt Bik Mater 69
Figure 3.38 0 Dan cle ect lod ssp a
and soe it th equation elite the ample x I
this way we find hat
wo F
— 645
aire pu
= x as
This isthe live displacement between th negative cloud
and he postive maceus I traditional to love q, positive
and speak about the dissem ofthe oxilor Without a
sing ore no incide wav) the oscilar il site st
ts resonance frequency. he presence o a feld whose
Frequency e less an a, ED and a) have he same sin,
which mean that the ocios can ollo the applied fore
{ie imphane with D. However, when a > ey the dis
placement a vin direction opposite to thao the nant
Fore, F, mus exist that returns the system tn gum,
Moreover, we cn reasonably expect ha for very small ie
placement fon gala (where F = De force wil
Beiinar ia note words, poro! Fa) versus wil ct
he ais atthe eli point (x = 0) and wil Be à
tight ine ver close on eher side, Ths for small displace
maison be suposed hat the restoring force has he form
FS 2h 2, whore isa kind of cale constant much ike a
String consent Once somehow momentarily disturbed, an
sion bound inthis way wil osito aboutit equ
Psion with a natura or resonant frequency Bien by
85 = Vii Jn, tere its mass. This the osito
fequeny of the rien stem
A material median is envisined as anascmblags in vac
nm. of very ret many polacizablesloms each of which ie
nai by comparo io ie wavelength oiga) and close o
is ncighboı. When a ighmane implag on nich a medium.
ach tom can be thought a a a client forced osea
Being driven by the time-varying cis field Et) ol e
sav, which is assumed here be api in edicion
Fie 330 à à mean repre fo sch an
shell fastened 10 a iatonary postive muele by Mental
Springs Even under the llaminaion of Bright sunlight, the
empitude ofthe oscillations wil be no reser than about
10" m The forse, )exeredom an electron carge y by
the Eifel ofa harmonie wave of freauency a bofıhe form
FEIN = ap Ecos an
face sin Ihe opposite direction, whic is why ha minos
sign Newton's Second Law provides the equation of moto
dan se som of the freee equals the man res the ach
acht 36H)
The Fr erm on the elt ste sing force, and second is
the opposing restoring Cee. Toasty his expression wi
Tv fo Bea fuctis whose sondere Very much
‘Steen fom elf Funhermon, we cu cpt ae
ern wi ie athe some MSA an Hr KO
35 pt Bik Mater 69
Figure 3.38 0 Dan cle ect lod ssp a
and soe it th equation elite the ample x I
this way we find hat
wo F
— 645
aire pu
= x as
This isthe live displacement between th negative cloud
and he postive maceus I traditional to love q, positive
and speak about the dissem ofthe oxilor Without a
sing ore no incide wav) the oscilar il site st
ts resonance frequency. he presence o a feld whose
Frequency e less an a, ED and a) have he same sin,
which mean that the ocios can ollo the applied fore
{ie imphane with D. However, when a > ey the dis
placement a vin direction opposite to thao the nant
70 Omer. Eectomgei Tea, Ptos ar
as re, E and terre 150 ul phase wih
Remember thar we ae ang at act ples where
for ay > ou e rave motion of the prie cn
pose hare I 180° ou of phase wih the Me and e
oles ado ag by a,
"Me dole moment ix equal 1 ie charge, anes is
2 ¿nn =
Don
ately 190 out-of phase wich te driving ore Te roi
«lets polation wil ereore be sity outa pas
tnt abe apple elec field Hence the delet constant
At fequencesinteningly blow resonance (os ~ 0") > 0.
ind of behavior, which cull repens ony par of
ha happens aonsthclese generally observed i al sons
‘We can et the lity of the analy à pente
pri p 187) made ofthe sample mri der.
Oe == a + ai
‘ere. ing» Be, the multiplica conan given
by C= dae tom, Naf. Figure 329 plocof a? 1)
fm à He discharge tbe nd he index of reiichon was
measured for each one (Tab
that the moon uen 1295 105 Har which prop
TABLE SS
wavelengths are those of a He discharge tube.
The corresponding indices were measured.
as re, E and terre 150 ul phase wih
Remember thar we ae ang at act ples where
for ay > ou e rave motion of the prie cn
pose hare I 180° ou of phase wih the Me and e
oles ado ag by a,
"Me dole moment ix equal 1 ie charge, anes is
2 ¿nn =
Don
ately 190 out-of phase wich te driving ore Te roi
«lets polation wil ereore be sity outa pas
tnt abe apple elec field Hence the delet constant
At fequencesinteningly blow resonance (os ~ 0") > 0.
ind of behavior, which cull repens ony par of
ha happens aonsthclese generally observed i al sons
‘We can et the lity of the analy à pente
pri p 187) made ofthe sample mri der.
Oe == a + ai
‘ere. ing» Be, the multiplica conan given
by C= dae tom, Naf. Figure 329 plocof a? 1)
fm à He discharge tbe nd he index of reiichon was
measured for each one (Tab
that the moon uen 1295 105 Har which prop
TABLE SS
wavelengths are those of a He discharge tube.
The corresponding indices were measured.
Aa ul, any ven subse wl aly undergo ere
raie fom > Hon < 1asıeHluninnin teen:
para ar several uch requetes would seem ses
<table 1 gence mars y supposing that ere ae 4
roles ont dans sch aes having a
plena EI la ae
NES hy
‘This i escena the same result as that arising from the
ganar mechanical nement, wih the exception thar some
‘tthe terns mist be centered. Accordingly the quactes
ny woul hen be he charters frequence at which an
eta sa or ni ee Te rm whch
Lown a ciao strength They es the emp that
should be placed on exch one of he modes. Since they mea
Sure the likelihood that à given atomic ration wil occur
A similar entrprettion l th tems seven required
classical, since agreement with the experimental data
demands tha they be less han any This i viously com
ay 1 he deinen ofthe faa edt Eg (3.71). One hen
‘oppone that a molecu has many osclatry modes but hat
tach thse has a inc natura requeey and eng
Notice that when w equals any ofthe characterise re
“pews, ni iscotimns, conta to acta) observation
Ths is simply the result of having neglected the damping
‘em which shoals have appeared inthe denominator ofthe
sam. incide, the damping. in pur. is tibusbl to ener
rl hehe forced oncle radio slid iid,
‘hd gases a igh pressure (=10° am). e itertume di
hoses ar roughly Limes less han hese of ag at standard
Seperate and pet. At a molles In hl
reali "fiction fore. Te effec ia damping ofthe
clore and a dissipation of thei enerey within he sub
Stace inthe form of “hen” (random molecular mio)
Had e included a dampin force proportional the speed
othe tom ny) i the equation of mein, the disp
‘Sor equation (371) would have Been
A Ys Expresion fn Tor anid meda wah as
pases, bese is arther complication tht must be ovenome it
{he uation it e aplc to dense sunt, Ess tom
dense terial wll also experience the indice tilde op by
thc reten, Coneqierly.am atom sess" in ation othe
applied Gel Et) another ci. namely, PL Ba. Without
sing atthe details here, can be shows that
>
“Ths ar we have been considering electron-ion
exclusively, Du the sme resul would have ben applicable
u inne bound o fed atomic ie ae we Int im ny
‘would be pled bythe considerably lage ion mass. Th
along iccronio polera trimponntoverahe emir
“paca speci, ie eombuionn frm ea polarization
Sica affect on regions ol resonant (uy = 4)
"The implications ofa complex index of retraction willbe
considered ater, I Section 48, Arthe moment we mie
sean forthe wos perforations crab
<=
Trsquencie ouside the visible egon ofthe spectrum (which
I why they ar in far, colors and amp} La pricy
la. lasts have effective natural frequencies above he vi
ble int lravile, where they Decome opague In css for
biche >> a by comparison, a? may be neiete in Ea
374) yielding an essential cons index ofrfracion over
that frequency region. For example, the important character
de fequences for pases os hs of abou 10
tm The mle ofthe vse range roy five times that
ty (oy = u deren and gradual increase with fe
‘glen seal evident in Fig. 3.40. Tics ale nor-
‘mal dispersion Inthe lcaviole region, a approach a
tral frequency, he esis wil begin fo esate. Their
ried by damping and a rong absorption of energy from the
raie fom > Hon < 1asıeHluninnin teen:
para ar several uch requetes would seem ses
<table 1 gence mars y supposing that ere ae 4
roles ont dans sch aes having a
plena EI la ae
NES hy
‘This i escena the same result as that arising from the
ganar mechanical nement, wih the exception thar some
‘tthe terns mist be centered. Accordingly the quactes
ny woul hen be he charters frequence at which an
eta sa or ni ee Te rm whch
Lown a ciao strength They es the emp that
should be placed on exch one of he modes. Since they mea
Sure the likelihood that à given atomic ration wil occur
A similar entrprettion l th tems seven required
classical, since agreement with the experimental data
demands tha they be less han any This i viously com
ay 1 he deinen ofthe faa edt Eg (3.71). One hen
‘oppone that a molecu has many osclatry modes but hat
tach thse has a inc natura requeey and eng
Notice that when w equals any ofthe characterise re
“pews, ni iscotimns, conta to acta) observation
Ths is simply the result of having neglected the damping
‘em which shoals have appeared inthe denominator ofthe
sam. incide, the damping. in pur. is tibusbl to ener
rl hehe forced oncle radio slid iid,
‘hd gases a igh pressure (=10° am). e itertume di
hoses ar roughly Limes less han hese of ag at standard
Seperate and pet. At a molles In hl
reali "fiction fore. Te effec ia damping ofthe
clore and a dissipation of thei enerey within he sub
Stace inthe form of “hen” (random molecular mio)
Had e included a dampin force proportional the speed
othe tom ny) i the equation of mein, the disp
‘Sor equation (371) would have Been
A Ys Expresion fn Tor anid meda wah as
pases, bese is arther complication tht must be ovenome it
{he uation it e aplc to dense sunt, Ess tom
dense terial wll also experience the indice tilde op by
thc reten, Coneqierly.am atom sess" in ation othe
applied Gel Et) another ci. namely, PL Ba. Without
sing atthe details here, can be shows that
>
“Ths ar we have been considering electron-ion
exclusively, Du the sme resul would have ben applicable
u inne bound o fed atomic ie ae we Int im ny
‘would be pled bythe considerably lage ion mass. Th
along iccronio polera trimponntoverahe emir
“paca speci, ie eombuionn frm ea polarization
Sica affect on regions ol resonant (uy = 4)
"The implications ofa complex index of retraction willbe
considered ater, I Section 48, Arthe moment we mie
sean forthe wos perforations crab
<=
Trsquencie ouside the visible egon ofthe spectrum (which
I why they ar in far, colors and amp} La pricy
la. lasts have effective natural frequencies above he vi
ble int lravile, where they Decome opague In css for
biche >> a by comparison, a? may be neiete in Ea
374) yielding an essential cons index ofrfracion over
that frequency region. For example, the important character
de fequences for pases os hs of abou 10
tm The mle ofthe vse range roy five times that
ty (oy = u deren and gradual increase with fe
‘glen seal evident in Fig. 3.40. Tics ale nor-
‘mal dispersion Inthe lcaviole region, a approach a
tral frequency, he esis wil begin fo esate. Their
ried by damping and a rong absorption of energy from the
sy = in E
nes sore dormant Te
nds Tre d/o gaie and the process poe a
pus rough ass prim, he Du come: a
ange (se Sesion 5.1) In contra when we ne à igi
tell ria comming dye solo wir abortion band in
350). A warces passes
5 the ral oxi ie re Io, in ie
inate. Molecals sich as RO and CO; have resonancia
Boch ie infra and ueavilet. When waters app with
ina piece ol gas during its manufacture. these molecalr
rab
existe. The presen of ones also resus if
Son. Figure 3,42 shows th
ines Abe even ower frequencies ademanes. plis
sein raspa a comparison, a pu
AS fal point tice hat i the dei
lass plate. This san iniging esa sit
‘der th behavor sain ter on. when we caste gr
nes sore dormant Te
nds Tre d/o gaie and the process poe a
pus rough ass prim, he Du come: a
ange (se Sesion 5.1) In contra when we ne à igi
tell ria comming dye solo wir abortion band in
350). A warces passes
5 the ral oxi ie re Io, in ie
inate. Molecals sich as RO and CO; have resonancia
Boch ie infra and ueavilet. When waters app with
ina piece ol gas during its manufacture. these molecalr
rab
existe. The presen of ones also resus if
Son. Figure 3,42 shows th
ines Abe even ower frequencies ademanes. plis
sein raspa a comparison, a pu
AS fal point tice hat i the dei
lass plate. This san iniging esa sit
‘der th behavor sain ter on. when we caste gr
rom ckettoni pletion the operative necest deter
‘mining na Classical. ane Imagine cctv ssllore
Whe the
Sateen prey eet rom hart
lator amps ar ine
‘noun he charges. Bco
ed, ai il doe an icresed
removed from the vane and converted no mechanical
‘dst thrall cit abs
radio at charctenstcteguenes ta phon}.
3.6 The Electromagnetic-Photon
Spectrum
ln 1867, whsn Maxell pued the Fist extensive account
‘fix Flctomagnctc Theory. he Tequeney and was oy
aviles Ahbaugh ka epion if major concern in Opt,
Fig. 3:43) The section enacts the
me overlapping) into which he specu ic
ain ceteris thre
Ge cual
aly divided
3.6.1 Radiofrequency Waves
in 1887, ig years alter Maxwells death, Heivich Hert,
thon profesor of physics atthe Technische Hochschule in
Kato. Germany, succeded in
rei dipole Far areeiinganenna hu
Sf wir witha bras koh on ane end an a fin copper point
fm the er. À small pork visible hetween the two ende
marked the deletion of an kon elector
Hers focinod the radiation, detomined it poliza
refleced and refait. caused 1 intrlre sein u
standing wave. and then even measured ts wa length con
theonderota
Te maven axed by Hert are now chui in hero
(ro many klomeen (0 0.3 ns}, Thee ac
ed bran amant fcc ens Forevam
wavelength of 3 x
could leisurely swing the proverbial charged pit al ad. in
a doing. produce à rather long. aot very strong, wave
Indesd, waves more than 18 milion miles long have bse
detected ring down toward Ban from outer space, The
‘mining na Classical. ane Imagine cctv ssllore
Whe the
Sateen prey eet rom hart
lator amps ar ine
‘noun he charges. Bco
ed, ai il doe an icresed
removed from the vane and converted no mechanical
‘dst thrall cit abs
radio at charctenstcteguenes ta phon}.
3.6 The Electromagnetic-Photon
Spectrum
ln 1867, whsn Maxell pued the Fist extensive account
‘fix Flctomagnctc Theory. he Tequeney and was oy
aviles Ahbaugh ka epion if major concern in Opt,
Fig. 3:43) The section enacts the
me overlapping) into which he specu ic
ain ceteris thre
Ge cual
aly divided
3.6.1 Radiofrequency Waves
in 1887, ig years alter Maxwells death, Heivich Hert,
thon profesor of physics atthe Technische Hochschule in
Kato. Germany, succeded in
rei dipole Far areeiinganenna hu
Sf wir witha bras koh on ane end an a fin copper point
fm the er. À small pork visible hetween the two ende
marked the deletion of an kon elector
Hers focinod the radiation, detomined it poliza
refleced and refait. caused 1 intrlre sein u
standing wave. and then even measured ts wa length con
theonderota
Te maven axed by Hert are now chui in hero
(ro many klomeen (0 0.3 ns}, Thee ac
ed bran amant fcc ens Forevam
wavelength of 3 x
could leisurely swing the proverbial charged pit al ad. in
a doing. produce à rather long. aot very strong, wave
Indesd, waves more than 18 milion miles long have bse
detected ring down toward Ban from outer space, The
Fire 343 Te détrempe sec
ihe frequency end ofthe band i ned for television and
radio broadcasting
AC MHc( Ha) aadofequene photon has an ears
06662 % 10 Lor 4310 eV a very small quantity by
any measut. The granular ature ofthe raiation i general
‘obscured and only «smooth transfer of radiofrequency ener
3.6.2 Microwaves
The microwave region extend rom abou 10" Hy wp io about
3% 10 Hi The comesponding wavelengths o rom ugh
ly 30 em to 1.0 sum. Radiation capable of penetring the
{ars alosphee rangos fom Is than Tem aout m.
‘Microwaves te therefore of interes in pas vehicle corm
icatone. a well a ado asronom. In particular, nesta
drogen aos. dated ose vn reposo! space eme
ecm (1420 Mit microwaves. À good deal of inform:
ahout he structure of our own and other gales has been
lene rom this parca mision
of motion of thee coment sloms—they can be made to
br and ole. Again, the energy associated with cier
motion is quantized, and molecules posess rotational and
ons. Only polar molecules wil experience frees via he E
Feld ofan incident elestomagnetic wave ha wil cause them
into aligument a oly bey can aor photo und
ake a vottonl ranston tan excited ut. Since museo
"re not abl swing arund easy we can an
Pate that they wil have low-frequency rotational resonances
1.0. rm, to mlromane, | em) For instance waler m0)
ects a polar (ce Fig 3.37), andi exposed o an elect
magnetic wave they wl swing around pin 1 a ed u
‘ih he aller ES This wil our wi particule ig
‘rat any one of ts rotational resonances. Consequely, water
‘molecules efficiently and dspativel absorb microwave rad
Ion ator near sh fogones. Ihe more oven 122
nonpola molecules, suchas carbon diode, hydrogen, nr
sen pe and mine. crack mae roainal rancios
ihe frequency end ofthe band i ned for television and
radio broadcasting
AC MHc( Ha) aadofequene photon has an ears
06662 % 10 Lor 4310 eV a very small quantity by
any measut. The granular ature ofthe raiation i general
‘obscured and only «smooth transfer of radiofrequency ener
3.6.2 Microwaves
The microwave region extend rom abou 10" Hy wp io about
3% 10 Hi The comesponding wavelengths o rom ugh
ly 30 em to 1.0 sum. Radiation capable of penetring the
{ars alosphee rangos fom Is than Tem aout m.
‘Microwaves te therefore of interes in pas vehicle corm
icatone. a well a ado asronom. In particular, nesta
drogen aos. dated ose vn reposo! space eme
ecm (1420 Mit microwaves. À good deal of inform:
ahout he structure of our own and other gales has been
lene rom this parca mision
of motion of thee coment sloms—they can be made to
br and ole. Again, the energy associated with cier
motion is quantized, and molecules posess rotational and
ons. Only polar molecules wil experience frees via he E
Feld ofan incident elestomagnetic wave ha wil cause them
into aligument a oly bey can aor photo und
ake a vottonl ranston tan excited ut. Since museo
"re not abl swing arund easy we can an
Pate that they wil have low-frequency rotational resonances
1.0. rm, to mlromane, | em) For instance waler m0)
ects a polar (ce Fig 3.37), andi exposed o an elect
magnetic wave they wl swing around pin 1 a ed u
‘ih he aller ES This wil our wi particule ig
‘rat any one of ts rotational resonances. Consequely, water
‘molecules efficiently and dspativel absorb microwave rad
Ion ator near sh fogones. Ihe more oven 122
nonpola molecules, suchas carbon diode, hydrogen, nr
sen pe and mine. crack mae roainal rancios
Moto
oy They ae le quie excel
Sihespesimental arrangements tht ae scaled up
oy They ae le quie excel
Sihespesimental arrangements tht ae scaled up
3.6.3 Infrared
The irn rim. eich eve orah rom 10 Hr
ao bout 3% DU He, wa it detected by the reused
ave pes, hi band of PM diia Les us ena rd
Tigh Te ined or IR. ion save ito ou seins
‘heme ht near he vise 78-300 the inter
ihe eme (SO nm) This gain arate
Josi division, and here nue ai the nomena
Hure Radiant energy at he ong-wavelength exes can Be
rate and aor IR Va mal aia
“The molecules of any object at temperature above
(see Seton 131.1), On he oer hr nrre is con
and the common lightbulb acially radiates fr more IR tha
Ih Like ll warm loaded creatures we 10 ae iar
int 3000 am. peaking inthe vicinisy of 10 000 nm. and
teyond. This emission sexed by sind spe
‘Sopes aswell aby some hr sy “eat senate ses
‘iret sch as CO; ste ha des ond
numero! energy level ach of which can he exited
iv are as ale nthe IR (1000 po 0.1 on), Mas
{he IR andre good absorbers, which ne vat IR col
Sunshine and fe he resul Pop Of era) every
Infrared radiant energy generally measured wid ade
‘hat espons 10 he Hea generated om absorption ol IR B=
lackoned surface. There ae, for example thrstocoupl
curate e Goly cel) pyreleiec, and aloe
Aetctrs. These in tum depend on tempecsure-depende
Polanzston and resistance respectively. The dtestr can
oped by yola cum stern to a cate ay be
produce an nstatacoxs lvoe IR ps (we pos
al sot of problems rom alt ramsfomner 1 ast po
ple Photographic films sense to car I ( 1300 a) ae
‘rocket launching Issa satelite, tha look ou ore
‘eats, and IR astronomica celts that look out in
‘wee, Tere ate “heating” misses guided hy TR nd
User and eescopes pring the heavens
Sal diferen the temperatures o objet and th
‘sueundings result in chute IR emission ha can be
sen to sorting» lrking bara. The CO, ter beca
ievelsof 100 W and more; widely uned in industry, ep
Sum. 230 am a real cobos by human
ha ati a su.
3.6.4 Light
ove hart of Frequencies from about 3.4 x 10" Hy to Eh
ales. (Dont forget synchro radiation wich i adie:
‘nt mecha
he re 1. gt ems tee to. On
The irn rim. eich eve orah rom 10 Hr
ao bout 3% DU He, wa it detected by the reused
ave pes, hi band of PM diia Les us ena rd
Tigh Te ined or IR. ion save ito ou seins
‘heme ht near he vise 78-300 the inter
ihe eme (SO nm) This gain arate
Josi division, and here nue ai the nomena
Hure Radiant energy at he ong-wavelength exes can Be
rate and aor IR Va mal aia
“The molecules of any object at temperature above
(see Seton 131.1), On he oer hr nrre is con
and the common lightbulb acially radiates fr more IR tha
Ih Like ll warm loaded creatures we 10 ae iar
int 3000 am. peaking inthe vicinisy of 10 000 nm. and
teyond. This emission sexed by sind spe
‘Sopes aswell aby some hr sy “eat senate ses
‘iret sch as CO; ste ha des ond
numero! energy level ach of which can he exited
iv are as ale nthe IR (1000 po 0.1 on), Mas
{he IR andre good absorbers, which ne vat IR col
Sunshine and fe he resul Pop Of era) every
Infrared radiant energy generally measured wid ade
‘hat espons 10 he Hea generated om absorption ol IR B=
lackoned surface. There ae, for example thrstocoupl
curate e Goly cel) pyreleiec, and aloe
Aetctrs. These in tum depend on tempecsure-depende
Polanzston and resistance respectively. The dtestr can
oped by yola cum stern to a cate ay be
produce an nstatacoxs lvoe IR ps (we pos
al sot of problems rom alt ramsfomner 1 ast po
ple Photographic films sense to car I ( 1300 a) ae
‘rocket launching Issa satelite, tha look ou ore
‘eats, and IR astronomica celts that look out in
‘wee, Tere ate “heating” misses guided hy TR nd
User and eescopes pring the heavens
Sal diferen the temperatures o objet and th
‘sueundings result in chute IR emission ha can be
sen to sorting» lrking bara. The CO, ter beca
ievelsof 100 W and more; widely uned in industry, ep
Sum. 230 am a real cobos by human
ha ati a su.
3.6.4 Light
ove hart of Frequencies from about 3.4 x 10" Hy to Eh
ales. (Dont forget synchro radiation wich i adie:
‘nt mecha
he re 1. gt ems tee to. On
tan incandescent materi hot lowing metal filament
the solar ireball, electrons are randomly seceleated and
Salen Cequentcllisions. The revaling bro emision
spectra alle theemalradlaton and major sure
te. comme fil tubo with some gas and pasan
tls discharge trough if the aors therein will Become
ied an raise. The emit ight characterise of the
‘sles of well deiod regusncy ands or inex. Such device
‘known sa gas discharge ale When the asic the kyptan
fee hear pray arto ers q
rN: whove aru wanclenih 6057902105 mm. has 3
‘ARH Baer) of only 000 47 mn. or bout 300 MB
Accordingly, un 1983 waste internal standard of
lenin (with 165076373 wavelengths equaling meer)
‘Newt was the ft 1 rocoguiz that white Hight at
ya minar fall te coors ofthe vibe spect, ha the
pra doesnot rat olor by allen white ht dicen
ee, aha Been thought or contri, at simply fam oat
TABLE 3.4 Approximate Frequency and
Vacuum Wavelength Ranges forthe
Various Colors
Tg i very concep OF wi
ception of arth i soci à road gi
#3 drama mall nf more ply in we ler tn a
Perd LA The human trae desertor pere
he vide mix of rence al wih abt are
mount of energy in ach porn Fat what we mean when
Ne peak abou le much of th solo hep
tram, wth no region predominating. Nonetheless, many di
recognize à piece of paper to be white whether is seen
indoors under incandescent light or outside under skit
‘even ho those whites are quie diferen ofc. er are
any pai of colored ig Bea eg 860m rd and 492
wil produce he sensaon of whiteness anlihe
‘ye cannot always distinguish one white from another an
TS A OOH
ewe zas
the solar ireball, electrons are randomly seceleated and
Salen Cequentcllisions. The revaling bro emision
spectra alle theemalradlaton and major sure
te. comme fil tubo with some gas and pasan
tls discharge trough if the aors therein will Become
ied an raise. The emit ight characterise of the
‘sles of well deiod regusncy ands or inex. Such device
‘known sa gas discharge ale When the asic the kyptan
fee hear pray arto ers q
rN: whove aru wanclenih 6057902105 mm. has 3
‘ARH Baer) of only 000 47 mn. or bout 300 MB
Accordingly, un 1983 waste internal standard of
lenin (with 165076373 wavelengths equaling meer)
‘Newt was the ft 1 rocoguiz that white Hight at
ya minar fall te coors ofthe vibe spect, ha the
pra doesnot rat olor by allen white ht dicen
ee, aha Been thought or contri, at simply fam oat
TABLE 3.4 Approximate Frequency and
Vacuum Wavelength Ranges forthe
Various Colors
Tg i very concep OF wi
ception of arth i soci à road gi
#3 drama mall nf more ply in we ler tn a
Perd LA The human trae desertor pere
he vide mix of rence al wih abt are
mount of energy in ach porn Fat what we mean when
Ne peak abou le much of th solo hep
tram, wth no region predominating. Nonetheless, many di
recognize à piece of paper to be white whether is seen
indoors under incandescent light or outside under skit
‘even ho those whites are quie diferen ofc. er are
any pai of colored ig Bea eg 860m rd and 492
wil produce he sensaon of whiteness anlihe
‘ye cannot always distinguish one white from another an
TS A OOH
ewe zas
78 aptes Promo ut
not frauen analy igh in its Hamnonie component the
‘a he sur cam analy sound ee Seton 7
Logis esse primar. oe various frequency regions
extending from alos 364 THe lor ed rang orange ye:
low. een and is. o sole at about 769 Ti (Table u
Colo is popen o he ih sl but a manifestation at
es Ba TOE
1d mo sy "plow Tight” but rer
entreguen minus an cvake the same color response
from the ye rin semor A bem of relight (peaking a.
‘40 THe) wll ru tive to inthe perception of
tote preis, we sr
ig ati een a yellow
Fed, gen. nd blue
right he 10" phonn m? s, we con gencrally expos the
{quantum mure of the energy ramport the thorozhiy
aed. However, very weak beans Since photos in he
‘produce effecis on a distincts individual has, the granular
13 wil become evident Research on human vision indiats
eee hese
3.6.5 Ultraviolet
Aion 1 an ju beyond ight in th specu the in
‘ole ion (opprosimch 8 x 10! Het about 34 10"
than cong er tonne atom nthe upper atmosphere
ar alum toner of the maria of many chemical ea
Tins, and ulraios rays Become importan in trigger
3. Fortunately, ne (0, inthe simoxpbere
shuns what would trab be a et ça of sla UV
The patclelhe aspects of
Ge. N miroorganis
show parut athe shorter wascengis, we i
hes had a lee removed bruit of cataracts can see UVA >
300 Im, nao toinects, ch x honeybees» rim
her ther eats cn ill repond LV Pigeons
imple, ae capable of scogmaing ptr minted y
UV and probably emplo that ally to navigate by he Sin
on overeat days
An st emitsa UV photon whe a lc makes og
jump down rom a highly excited ae For example tbe oa
{ros leven of asodium tom canbe rt o higher so
at 51 eV, andthe som is jonized I the fon pure
to the ground state, mos likely in a ser of jump, each
‘ein inthe cion of à hate I in poste, Rome
radiating single 5.1-eV UV photon, Even more energetic UV
an he pen wen he inne, italy Pound electron ot
Tumor valence electrons of old atom can beat
important source of color igh. Bu when bes ame toes
‘edna aire in he proces of ret chemical bords
that hol he tin tether, Comegsendy. the elestons e
ea more igh ond. and ti molecular exited sats
hist up ith
UV: Molec nih atnsphet. chit
not frauen analy igh in its Hamnonie component the
‘a he sur cam analy sound ee Seton 7
Logis esse primar. oe various frequency regions
extending from alos 364 THe lor ed rang orange ye:
low. een and is. o sole at about 769 Ti (Table u
Colo is popen o he ih sl but a manifestation at
es Ba TOE
1d mo sy "plow Tight” but rer
entreguen minus an cvake the same color response
from the ye rin semor A bem of relight (peaking a.
‘40 THe) wll ru tive to inthe perception of
tote preis, we sr
ig ati een a yellow
Fed, gen. nd blue
right he 10" phonn m? s, we con gencrally expos the
{quantum mure of the energy ramport the thorozhiy
aed. However, very weak beans Since photos in he
‘produce effecis on a distincts individual has, the granular
13 wil become evident Research on human vision indiats
eee hese
3.6.5 Ultraviolet
Aion 1 an ju beyond ight in th specu the in
‘ole ion (opprosimch 8 x 10! Het about 34 10"
than cong er tonne atom nthe upper atmosphere
ar alum toner of the maria of many chemical ea
Tins, and ulraios rays Become importan in trigger
3. Fortunately, ne (0, inthe simoxpbere
shuns what would trab be a et ça of sla UV
The patclelhe aspects of
Ge. N miroorganis
show parut athe shorter wascengis, we i
hes had a lee removed bruit of cataracts can see UVA >
300 Im, nao toinects, ch x honeybees» rim
her ther eats cn ill repond LV Pigeons
imple, ae capable of scogmaing ptr minted y
UV and probably emplo that ally to navigate by he Sin
on overeat days
An st emitsa UV photon whe a lc makes og
jump down rom a highly excited ae For example tbe oa
{ros leven of asodium tom canbe rt o higher so
at 51 eV, andthe som is jonized I the fon pure
to the ground state, mos likely in a ser of jump, each
‘ein inthe cion of à hate I in poste, Rome
radiating single 5.1-eV UV photon, Even more energetic UV
an he pen wen he inne, italy Pound electron ot
Tumor valence electrons of old atom can beat
important source of color igh. Bu when bes ame toes
‘edna aire in he proces of ret chemical bords
that hol he tin tether, Comegsendy. the elestons e
ea more igh ond. and ti molecular exited sats
hist up ith
UV: Molec nih atnsphet. chit
8.03, ©;
‘Nowadays here an arab photographs ls and
siroscopes, UV orbiting cles telescopes, synchroton
res and se,
and HO, have jos his on of eletonic o
3.6.6 X-rays
X rave were rather frvitousy discosered in 195 hy Wil
‘elm Conrad Ringen (1845 1023). Extending in frequency
feom roughly 24 X 10° Hy 40.5 x 10° Hz. they have
rem shor wavelengths: mow us smaller han an tom,
Their phetu energies (10 eV 1002 MeV) ate lr enough
‘aly granule fashion, alot ike hat of energy. On of
Sc ment practical mechanism for producing X ra) the
spi dceeraon of high-speed charged particles The resi
ing brosd-Iroqueney bremstrhlung (German for "rakng
tition” aies when à ea o energie elects i ed
Aa material argo such aa coppe plate, Colon wt the
{imate pende defection the hsm lectons: which
tn ade ray photons,
Tw addition, the atoms of the target mas became ionized
ring the bombardment, Should thst ocur trough removal
si emit Xray ay the ect loud tures to the pod
Sze eos eme sso are pectic enh tr
36 ane Eeevomape Pon Serum 79
ing its norgy-level rcs, and cordingly
Traditional medical laweiography generally produces
Vie mors thin simple shadow castings. thr than photo.
mager ig detailed pre ll sor sigs, om
phone fasion pelts to Seta sources such a he Son
“stat paar nd black oles objets tm
erates of milion of depre tht emit predaminany int
Koray rei
Orting X-ray telscopos Inve given una
oe on the Universe tre photo) Tee ae Kay
Ton gang an iets und wor ones X
fp orge ln O8 a pray acto Lawrence Linemoro
Nero aborto succeed producing rer rio a
a wavelength of 216 um. Abo hi mor certe m
the extreme uraviler (XUV) its clase enough othe ay
region uty the fist sot Xray laser
3.6.7 Gamma Rays
Gam rays an the highest energy (10 SV to about 10” eV
ite by panico underoing transitions wii he some
‘Nowadays here an arab photographs ls and
siroscopes, UV orbiting cles telescopes, synchroton
res and se,
and HO, have jos his on of eletonic o
3.6.6 X-rays
X rave were rather frvitousy discosered in 195 hy Wil
‘elm Conrad Ringen (1845 1023). Extending in frequency
feom roughly 24 X 10° Hy 40.5 x 10° Hz. they have
rem shor wavelengths: mow us smaller han an tom,
Their phetu energies (10 eV 1002 MeV) ate lr enough
‘aly granule fashion, alot ike hat of energy. On of
Sc ment practical mechanism for producing X ra) the
spi dceeraon of high-speed charged particles The resi
ing brosd-Iroqueney bremstrhlung (German for "rakng
tition” aies when à ea o energie elects i ed
Aa material argo such aa coppe plate, Colon wt the
{imate pende defection the hsm lectons: which
tn ade ray photons,
Tw addition, the atoms of the target mas became ionized
ring the bombardment, Should thst ocur trough removal
si emit Xray ay the ect loud tures to the pod
Sze eos eme sso are pectic enh tr
36 ane Eeevomape Pon Serum 79
ing its norgy-level rcs, and cordingly
Traditional medical laweiography generally produces
Vie mors thin simple shadow castings. thr than photo.
mager ig detailed pre ll sor sigs, om
phone fasion pelts to Seta sources such a he Son
“stat paar nd black oles objets tm
erates of milion of depre tht emit predaminany int
Koray rei
Orting X-ray telscopos Inve given una
oe on the Universe tre photo) Tee ae Kay
Ton gang an iets und wor ones X
fp orge ln O8 a pray acto Lawrence Linemoro
Nero aborto succeed producing rer rio a
a wavelength of 216 um. Abo hi mor certe m
the extreme uraviler (XUV) its clase enough othe ay
region uty the fist sot Xray laser
3.6.7 Gamma Rays
Gam rays an the highest energy (10 SV to about 10” eV
ite by panico underoing transitions wii he some
10 Omen 3
da an e detected ih ite il A ie am m
max io sal hai I ow extremely eu 1
"We have gone fee fom te rodifregueney wei
far rom the logariteriey corts of the pce
quand. bat her shat we
pra ha we ae” wil depend om
3.7 Quantum Field Theory _
rene a ac of stromag iteration around sl that
ihe line Rod, which ia reprscataton ofthe way the
soma Itercien reveals Hel a matrneopie
Tove The we er el ct spatial concep
summazing th interaction among. charges. Through
inerte Scsi, and vice vera. Whit began a
‘mapping oe force diia ubatever sabs) became
ue sccms sraighforward even many questions cometo
1 does th happen? saying aa va
onli span the voué of ope: ight was an electro
gee eave ithe eecromayieie field SNR =
SS ER EM sping MSN
Ts one shown in ig. 335, miga be
eek stromag
ine om ore vel. Bu t's arly what one would sll ach
‘nave which sso Real mathematclly. i ot gute
non of Escoge Theory o be design of
Som am he mete Pick
Ford repesnatin war weh mie escape
Anais dre nr fl
{ally ausoandforeveryihing being measure, ui was bl
Toor to the exceedingly ne gran saute of dk
phensmenen Using thermodynamic ungen, Ein pro:
pol tt ci nd ge elds were quid, a hy
Sold decades Before the ist mas cu dere
Today. we are guide by Quantum Mechanics, highly
and predice power bit is nonetheless disconcerting
a ions, Quant Feld Theory (QF.
sais fons the most fundamental and arguably 1
ina completely natura nay by quan ins
Ihe eetromagneie Reid The apurer ication fis
da an e detected ih ite il A ie am m
max io sal hai I ow extremely eu 1
"We have gone fee fom te rodifregueney wei
far rom the logariteriey corts of the pce
quand. bat her shat we
pra ha we ae” wil depend om
3.7 Quantum Field Theory _
rene a ac of stromag iteration around sl that
ihe line Rod, which ia reprscataton ofthe way the
soma Itercien reveals Hel a matrneopie
Tove The we er el ct spatial concep
summazing th interaction among. charges. Through
inerte Scsi, and vice vera. Whit began a
‘mapping oe force diia ubatever sabs) became
ue sccms sraighforward even many questions cometo
1 does th happen? saying aa va
onli span the voué of ope: ight was an electro
gee eave ithe eecromayieie field SNR =
SS ER EM sping MSN
Ts one shown in ig. 335, miga be
eek stromag
ine om ore vel. Bu t's arly what one would sll ach
‘nave which sso Real mathematclly. i ot gute
non of Escoge Theory o be design of
Som am he mete Pick
Ford repesnatin war weh mie escape
Anais dre nr fl
{ally ausoandforeveryihing being measure, ui was bl
Toor to the exceedingly ne gran saute of dk
phensmenen Using thermodynamic ungen, Ein pro:
pol tt ci nd ge elds were quid, a hy
Sold decades Before the ist mas cu dere
Today. we are guide by Quantum Mechanics, highly
and predice power bit is nonetheless disconcerting
a ions, Quant Feld Theory (QF.
sais fons the most fundamental and arguably 1
ina completely natura nay by quan ins
Ihe eetromagneie Reid The apurer ication fis
fat ll mieropaices viginate nthe same way fom thei
‘en individual els the field's the thing ac were. Thus
the electrons the quantum of the eletrn fed the proton it
the quantum ofthe proton field nd so fort, Fling in th
alls hs sc ase oF DEF mu of
There ae two distin philosophical cuen in conte
Fin QE he el center and Ihe article cmd ne
Bee semered view, lls an the fundamental ns, par
ter are just the quanta of the ts. nh parlent
si, purtile ar the fundamental entities, fields ar just
‘he macroscopic eerent slate ef pares The cl ad
tin goes hack to L. de Broglie (1923). E Schrodinger
(he quantum mechanical variant sometimes called Wave
Mechanics The particle tradition bogan wi early work
a We Hehenhers (1928) although te spirita mentor was
PAM. Dirac who st the parle agenda with is theory of
‘eckson postre pir, The puialar ofihot of OFT tar
he elchemagneike interaction called” Quantum
ecrodynamics(QED). and it too he is parice-cetered
and feld.cemered proponents. Some af the had dss of
{QED have been made accesible on ie het by RP:
man, and isofr as thy lumina Optic we explore
‘hem tern thinsest¢p. 137
omemporny pays by say of GET holds ar lid
‘ne quantized; that ach of the fundamental Four Forces
(Gentunional Etcromagnenc, Stor and Weak) i edit
«by special ind of Rel panico These mesenger bosons
“ve continuons absorbed and emite by the Encractng
mara paies (cecrons. protons, ete). This ongoing
rame sth meracnen The meting parco le ck
Se Reihe vital photon, Thi moves mesenger u
ele athe pcs oflgh and anspor omentum acer:
When two electro pel an noir, a electron and pro
are beings ease ofthe action oforce. Te niessengor
parce o the elecromagne foros ae called ral pho
sa never escape to be detected dit y Some inunumen,
however anti that philosophically and however ar
makes nel orextence. indeed irl pho
‘eration They ae catre for meaphyal
stasis el tobe determined
themvslves as continuous eld provided thy can group in
‘sy luge numbers. Fundamental parles have an intime
tracers, Quantum Theor ell ws te déc eld
ur an occur only oros are medie by mowsnger
paces ing angular moments gl nego mules of
hie (ie, 0, 120 20/20. WI, 0.) The angular
Momentum of he visual photon is Wh 22: pin pa.
Sole The exssedingly important lass finest ta Re
Spin. mesenger are Known a gauge frees. andthe ic
tromagaetc ore the model oral the gage forces. Tey,
distance underuooé vi eno les
mysterious exchange of vna! particles ut
Highly predictive mathematical theory is in place that
esis the phenomenon,
‘en individual els the field's the thing ac were. Thus
the electrons the quantum of the eletrn fed the proton it
the quantum ofthe proton field nd so fort, Fling in th
alls hs sc ase oF DEF mu of
There ae two distin philosophical cuen in conte
Fin QE he el center and Ihe article cmd ne
Bee semered view, lls an the fundamental ns, par
ter are just the quanta of the ts. nh parlent
si, purtile ar the fundamental entities, fields ar just
‘he macroscopic eerent slate ef pares The cl ad
tin goes hack to L. de Broglie (1923). E Schrodinger
(he quantum mechanical variant sometimes called Wave
Mechanics The particle tradition bogan wi early work
a We Hehenhers (1928) although te spirita mentor was
PAM. Dirac who st the parle agenda with is theory of
‘eckson postre pir, The puialar ofihot of OFT tar
he elchemagneike interaction called” Quantum
ecrodynamics(QED). and it too he is parice-cetered
and feld.cemered proponents. Some af the had dss of
{QED have been made accesible on ie het by RP:
man, and isofr as thy lumina Optic we explore
‘hem tern thinsest¢p. 137
omemporny pays by say of GET holds ar lid
‘ne quantized; that ach of the fundamental Four Forces
(Gentunional Etcromagnenc, Stor and Weak) i edit
«by special ind of Rel panico These mesenger bosons
“ve continuons absorbed and emite by the Encractng
mara paies (cecrons. protons, ete). This ongoing
rame sth meracnen The meting parco le ck
Se Reihe vital photon, Thi moves mesenger u
ele athe pcs oflgh and anspor omentum acer:
When two electro pel an noir, a electron and pro
are beings ease ofthe action oforce. Te niessengor
parce o the elecromagne foros ae called ral pho
sa never escape to be detected dit y Some inunumen,
however anti that philosophically and however ar
makes nel orextence. indeed irl pho
‘eration They ae catre for meaphyal
stasis el tobe determined
themvslves as continuous eld provided thy can group in
‘sy luge numbers. Fundamental parles have an intime
tracers, Quantum Theor ell ws te déc eld
ur an occur only oros are medie by mowsnger
paces ing angular moments gl nego mules of
hie (ie, 0, 120 20/20. WI, 0.) The angular
Momentum of he visual photon is Wh 22: pin pa.
Sole The exssedingly important lass finest ta Re
Spin. mesenger are Known a gauge frees. andthe ic
tromagaetc ore the model oral the gage forces. Tey,
distance underuooé vi eno les
mysterious exchange of vna! particles ut
Highly predictive mathematical theory is in place that
esis the phenomenon,
22 chapter te
PROBLEMS
BA Cro ci a 32755 nmtarmon Eee when etc iia
rar} From of heme? ty Domine bibi rie vs
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36 Tous
PROBLEMS
BA Cro ci a 32755 nmtarmon Eee when etc iia
rar} From of heme? ty Domine bibi rie vs
32 ea pos Ta ET at oe
A we ein ihe ove ane
241% Stow tame gen frat lh pci pa
312° Ware presi
36 Tous
213° Poets tian of ahamenic EM wane ire
A147 Al bb ps. 20 o nn cy ano
FAS" Conc aient m
RIB On acrgs: te et AER power AE ye
347 A say polarized bon lie wave islam
as
she ste
19° A ler vies plas of Edition in race ing
320 A LOW setos Bam ato Amine ih
AZI" A loa of ows vin ens Nina per cb
3:23" thw many loto pe sand. EM rn 100
IUCN ih a aw 3A onu
2.25" Aviston wea ie poi en mer
3.26 Using ens a
3.28 Conieranstecrngetic wave ning onan
3.29" Dri aereo tr ash eset when then
A cence HOW a LID
3.31 Mara msi o ths oye
A147 Al bb ps. 20 o nn cy ano
FAS" Conc aient m
RIB On acrgs: te et AER power AE ye
347 A say polarized bon lie wave islam
as
she ste
19° A ler vies plas of Edition in race ing
320 A LOW setos Bam ato Amine ih
AZI" A loa of ows vin ens Nina per cb
3:23" thw many loto pe sand. EM rn 100
IUCN ih a aw 3A onu
2.25" Aviston wea ie poi en mer
3.26 Using ens a
3.28 Conieranstecrngetic wave ning onan
3.29" Dri aereo tr ash eset when then
A cence HOW a LID
3.31 Mara msi o ths oye
2:32" A saris ped pind be o igh of com
339° à sm oe Tene win
3.34 Wha fone on he menge il exe ih 0 1350
3.39 A are nn Zi ar sis 20
2226 Conde he ph an arm rating im ac wi
2.39 Conor non moving charge en Fig, 2268
Fa Ra a a TTRTE
340" ©
3417 Dam
3.42 re pere pa poche (SO
249 Mean eli lier
3:49" Yellow ti tm sam
3:46" Algas ae om pont A tpn a vacuum Sp
meson ga fon A tod ut ls in pls
3.47 Tre ow raperos
348 Siar
249° 1 be now cie nee ut sac
Resume ach EH
339° à sm oe Tene win
3.34 Wha fone on he menge il exe ih 0 1350
3.39 A are nn Zi ar sis 20
2226 Conde he ph an arm rating im ac wi
2.39 Conor non moving charge en Fig, 2268
Fa Ra a a TTRTE
340" ©
3417 Dam
3.42 re pere pa poche (SO
249 Mean eli lier
3:49" Yellow ti tm sam
3:46" Algas ae om pont A tpn a vacuum Sp
meson ga fon A tod ut ls in pls
3.47 Tre ow raperos
348 Siar
249° 1 be now cie nee ut sac
Resume ach EH
351° take Fy (371) a hick ot the
352 Te onan sueno of eal ps be UV lay or 3.86" Crys
597 Stow dh Fy 3.0) cant orien a 357° Uo 171 Seiner dese esqui
erection . Canc Etoo >> Cash ons
seth Cae lon In ght of 1 li
8 Reto rie probe ral Ut ergo of ener. Val be minima fc: ofthe amen
352 Te onan sueno of eal ps be UV lay or 3.86" Crys
597 Stow dh Fy 3.0) cant orien a 357° Uo 171 Seiner dese esqui
erection . Canc Etoo >> Cash ons
seth Cae lon In ght of 1 li
8 Reto rie probe ral Ut ergo of ener. Val be minima fc: ofthe amen
The Propagation
of Light
4.1 Introduction —_ Bon ar macoeni manne of cti erring
of Light
4.1 Introduction —_ Bon ar macoeni manne of cti erring
ira €or Sgt rere a regente sad ar rn“
(Sr Teh ay sated à oy Bo ate my De 2
"he as tenuous, so the Beam i very ie acne unless
pass rula emendogsvoleme 0 a
mt e
this.
Fore 42. Aloe wove, ce Fa et nes aos
42 Pain nun 87
The amples of the ground-state vibrations, and hee
fore the amplitudes of the stc lig innen wih Ie
ency because a Whe molecules have line eons
inthe UV. The closer the driving frequency iso arena
the move vigorously the ocio respondo. o. ve ih
strongly sets laterally out ofthe bem, av ble o
hy ever ee punt cosa et
beam tha avers the gs will thos hericherin he rend of
the spectrum, wil the igh steed ot slight ot having
Thain arts wy the sky Be
‘Long Before Quantum Meshanis, Lond Rayleigh 187i
"sin a simple argument based on dimensional anayals (300
Prohiem 4.) he corety consid Ut the intensity of the
ester light vos proportions to 1/ and erfor nro
swath. Before tit work, wan widely eleve that
Sky was ble because of searing rom minute du piles
Since thi me scaeing involving particles aller an a
‘Rayleigh Saterng. Atoms and ordinary molecules che ill
since he ate ae enti of nanometer in diameter, where
‘yen a Dlucjay s feathers, the Bue-ailed skinke's Bue ta
und the Raboon’s Blue buttocks ae all colored via Ray
aus o alos al she be, much of the given, and eve oe
ofthe purple coloration. Seattering rom he ny alveolar sel
in the bars ofthe jays eater make Die, wheres ar
o's green a bend of yellow arising from presea,
abs (p13) nd Due vi sete
Ase will seein a moment, dense uniform subis will
not appreciably seater laterally, and hat applies o mach of
the lower anmasghere. Afir al if lu it were sony
ane ot ta vla farol mountain woud apre rt
cir. Even in ie middle regions of the aumonpher, the
Sensi peat enough suppress Raleigh Sater. oe
resin tidy can ing dentin. Aacwation on Ga
more none direction han another M.Smolsbows I)
and A Einstein (1910) independently provides he ba ds
forthe theory ol catering rom these factions, hic
(Sr Teh ay sated à oy Bo ate my De 2
"he as tenuous, so the Beam i very ie acne unless
pass rula emendogsvoleme 0 a
mt e
this.
Fore 42. Aloe wove, ce Fa et nes aos
42 Pain nun 87
The amples of the ground-state vibrations, and hee
fore the amplitudes of the stc lig innen wih Ie
ency because a Whe molecules have line eons
inthe UV. The closer the driving frequency iso arena
the move vigorously the ocio respondo. o. ve ih
strongly sets laterally out ofthe bem, av ble o
hy ever ee punt cosa et
beam tha avers the gs will thos hericherin he rend of
the spectrum, wil the igh steed ot slight ot having
Thain arts wy the sky Be
‘Long Before Quantum Meshanis, Lond Rayleigh 187i
"sin a simple argument based on dimensional anayals (300
Prohiem 4.) he corety consid Ut the intensity of the
ester light vos proportions to 1/ and erfor nro
swath. Before tit work, wan widely eleve that
Sky was ble because of searing rom minute du piles
Since thi me scaeing involving particles aller an a
‘Rayleigh Saterng. Atoms and ordinary molecules che ill
since he ate ae enti of nanometer in diameter, where
‘yen a Dlucjay s feathers, the Bue-ailed skinke's Bue ta
und the Raboon’s Blue buttocks ae all colored via Ray
aus o alos al she be, much of the given, and eve oe
ofthe purple coloration. Seattering rom he ny alveolar sel
in the bars ofthe jays eater make Die, wheres ar
o's green a bend of yellow arising from presea,
abs (p13) nd Due vi sete
Ase will seein a moment, dense uniform subis will
not appreciably seater laterally, and hat applies o mach of
the lower anmasghere. Afir al if lu it were sony
ane ot ta vla farol mountain woud apre rt
cir. Even in ie middle regions of the aumonpher, the
Sensi peat enough suppress Raleigh Sater. oe
resin tidy can ing dentin. Aacwation on Ga
more none direction han another M.Smolsbows I)
and A Einstein (1910) independently provides he ba ds
forthe theory ol catering rom these factions, hic
vcs similar results to those of Rayleigh, Seater
great itunes in medium, such asthe glass fiber of
Tink p97
tions Wills! a amanphere. he dy
pS ra rc chnescof attr mor o tam des
4.2.1 Scattering and Interference
Indeme mst
Satire cleciromagnsic wavele Thene wavelet overlap
rn =
Asal de denser the substance trough which Hight
hy thao, we must examine de inerte aking p
Tener a sca Boe discs p20) a vil De
sum oe to ave val
ace This exteme canes called ttl constate interfer
fence. When the phase once eich 180" the waves teal
ie imerference 2214
ee random arayed in pace so thatthe phases of he sc
relation to on another nd there nosed pate
ion bee
iia enous ga Fi da parallel bea light i
nero, Tt sation curs whe he
great itunes in medium, such asthe glass fiber of
Tink p97
tions Wills! a amanphere. he dy
pS ra rc chnescof attr mor o tam des
4.2.1 Scattering and Interference
Indeme mst
Satire cleciromagnsic wavele Thene wavelet overlap
rn =
Asal de denser the substance trough which Hight
hy thao, we must examine de inerte aking p
Tener a sca Boe discs p20) a vil De
sum oe to ave val
ace This exteme canes called ttl constate interfer
fence. When the phase once eich 180" the waves teal
ie imerference 2214
ee random arayed in pace so thatthe phases of he sc
relation to on another nd there nosed pate
ion bee
iia enous ga Fi da parallel bea light i
nero, Tt sation curs whe he
tance compone of plane waves ominates = group of
vie puse moletlo»A conining progression oF pr
creais ach molec, ich, tar rs gst al
clin, and a pacas out 10 same Tal pat P-
‘esas ths legs of hirsndvidul pas to Pier ect
Ahead of other while some are Behind, amd tha by substan
atenga (Fg. 4 36) Fer word, he pss
lol the wavelets at Puller really (Remeber tba the mol
lesa alo cv eel et a changes Be pecs 5
some destrucivel and th shifting random hodgspadg of
‘nslaping wavelets lfetvly averages aay he inter
<a Random, widely spaced scatterer driven by am inciden
‘fone another in all directions except forward. Lateral
seared light unimpeded by interference, reams oof the
mee wp inthe Earth's tens highraitude atmosphere
That th cate iradiane sould depen on U/A sexe
iy Gen y tring to e concepto! dipole ala See
ton 34.3. Each molcoule ls taken a un élection oscilar
2 sume vo e Independent of one ander and cach adh
in son with a, (361 The satire lee fil ae
«nia independent, and thee ls no itrernce Ita.
Acca the net aden at Ps the
‘idl eacrer th radiance ven by Fy (387). und
bi som ofthe
The advent of the laver has made it nv cy to
avere Raleigh Scanerng dite} in low pressure ques
Forward Propagation
po pms aca
os rel Fi hi
ih an Incoming primary plan wave—a soi ar represents
mary wavefront impinges on molecule À, which be
ater a spherical wate. For he moment, suppose the
E Be u
vie puse moletlo»A conining progression oF pr
creais ach molec, ich, tar rs gst al
clin, and a pacas out 10 same Tal pat P-
‘esas ths legs of hirsndvidul pas to Pier ect
Ahead of other while some are Behind, amd tha by substan
atenga (Fg. 4 36) Fer word, he pss
lol the wavelets at Puller really (Remeber tba the mol
lesa alo cv eel et a changes Be pecs 5
some destrucivel and th shifting random hodgspadg of
‘nslaping wavelets lfetvly averages aay he inter
<a Random, widely spaced scatterer driven by am inciden
‘fone another in all directions except forward. Lateral
seared light unimpeded by interference, reams oof the
mee wp inthe Earth's tens highraitude atmosphere
That th cate iradiane sould depen on U/A sexe
iy Gen y tring to e concepto! dipole ala See
ton 34.3. Each molcoule ls taken a un élection oscilar
2 sume vo e Independent of one ander and cach adh
in son with a, (361 The satire lee fil ae
«nia independent, and thee ls no itrernce Ita.
Acca the net aden at Ps the
‘idl eacrer th radiance ven by Fy (387). und
bi som ofthe
The advent of the laver has made it nv cy to
avere Raleigh Scanerng dite} in low pressure ques
Forward Propagation
po pms aca
os rel Fi hi
ih an Incoming primary plan wave—a soi ar represents
mary wavefront impinges on molecule À, which be
ater a spherical wate. For he moment, suppose the
E Be u
90 Copter A rest Li
begin. race au (a negative Fe inc
Being diver peak a poire Efe), Pa (
‘uate bat matching 0
‘which must aho be outs. phase hy 180° In (c) and id), we
sc e pin al of hs ame, ho wavelet a mar
tion woul be ue or auch wavelet spades oth how
Because of th symm ina bythe am call
‘the scared wavelet add constructively with eachother in
‘he forward direction,
thr. The incident ato
4.2.2 The Transmission of Light Through Dense
Media
amount of sr inthe egion und
arche cn side, comal à great man) meu
ssc gS IC a TES in ey Inka
pried by à proortonse tores ne de teat
Arne ange i he Ban mme st SP ac
sth 300 mm) rad er
{C3 meant propel be sumed ave a some Pin P
sully ne quid nd olds where ators ne [Om
‘height nam efetvelyencoeters ior mem wi
that much independent ofthe acangemeat af the mole
ihr Sins Lite a ne Hit ends up scared laterals
or closand tna dense humogenrou medion,
one together scaner. All
han ie caeres and Unir poing. thee wil y ala
he pis of mesi ttt ego euch bers arce
‘ach somewhat out-of-phase with the next, so thatthe sum
(bic wi be deren rom pots to poi wil ebay be
Pare 4,7. La) ana rt yt Arty tod wes re
begin. race au (a negative Fe inc
Being diver peak a poire Efe), Pa (
‘uate bat matching 0
‘which must aho be outs. phase hy 180° In (c) and id), we
sc e pin al of hs ame, ho wavelet a mar
tion woul be ue or auch wavelet spades oth how
Because of th symm ina bythe am call
‘the scared wavelet add constructively with eachother in
‘he forward direction,
thr. The incident ato
4.2.2 The Transmission of Light Through Dense
Media
amount of sr inthe egion und
arche cn side, comal à great man) meu
ssc gS IC a TES in ey Inka
pried by à proortonse tores ne de teat
Arne ange i he Ban mme st SP ac
sth 300 mm) rad er
{C3 meant propel be sumed ave a some Pin P
sully ne quid nd olds where ators ne [Om
‘height nam efetvelyencoeters ior mem wi
that much independent ofthe acangemeat af the mole
ihr Sins Lite a ne Hit ends up scared laterals
or closand tna dense humogenrou medion,
one together scaner. All
han ie caeres and Unir poing. thee wil y ala
he pis of mesi ttt ego euch bers arce
‘ach somewhat out-of-phase with the next, so thatthe sum
(bic wi be deren rom pots to poi wil ebay be
Pare 4,7. La) ana rt yt Arty tod wes re
RT
ESA
Pv
4
X
ES
À
ESA
Pv
4
X
ES
À
82 Chapter
ge desde sed
and the direc eam wil
si ao seater ight cal bt Sry weal, Gond cyl
Zeta wre a scars und when thee we small oi
he gem moonstone the merging pt wil he ba
1 1849 Jo Tyodall experimentally ed the sane
race by mal parle He and dat a es athe
aril incremed (rom a aston ol wavelength, e
RS MOS po
serios. Orio cloud In hey ts tothe at
aio. The same a ofthe mi
‘When number of molecle in particle sl, bey
ae allele 0 ne another and ac non; heir manele
ree ster propeionstly
The ori any of sete Mom sper pales
ng Se was Tia pushed Wy Cay Mic 908 Mie
tik size excoeds A. Reasonably enough, Rayleigh Seating
isthe stall size ing eave ol Mie Seatering
large water droplets. tae same way. some mnenpsmive pla»
i fod conics and whe garage-bag past lok pale
ite light The garbage Bug iordr o be made pag
one oF the ed end othe
4.2.3 Transmission and the Index
of Refraction
a ongoing epeiise prensa watering and rain
Fach such even tac aphase shit inte igh fl
ich imately shows ap an a bit he apparent phase
That comenponds o an inde of tfraction forthe median
y = e or which cathe th nc ven ouh photos ei
Tosce hom hin comes aot return Fig 5 Rel
the scaler vet al combine o lane inthe onwards
‘Seton to form what might ox e alle the secondary
sur. Por empirical reasons one we con aici hat
Secondary wave will combine with what tothe prima
men mes propagate ron e
era old withthe perce the medium an ce
tainly poses an index of eration ers. There
a may appear to havea pase velo tes than qu
do. or ever rer ea The ew ti apparent oni
ti eid ts he Phase lationship between te second
‘ng me th primary diane ony ehe os
frequencies. Ax Me fequency ofthe cletomagncie ie
nc, he owas wi fa hd sen
heran as lg wil each OF ocres er
save the panivile_sharactexc ale. Problem &
phare pha ls fora dang ven car an Fi
13 sammie the est
{adn othe aps hn i ber fet ha must de
fen aaa ware el ap te oscil
ge desde sed
and the direc eam wil
si ao seater ight cal bt Sry weal, Gond cyl
Zeta wre a scars und when thee we small oi
he gem moonstone the merging pt wil he ba
1 1849 Jo Tyodall experimentally ed the sane
race by mal parle He and dat a es athe
aril incremed (rom a aston ol wavelength, e
RS MOS po
serios. Orio cloud In hey ts tothe at
aio. The same a ofthe mi
‘When number of molecle in particle sl, bey
ae allele 0 ne another and ac non; heir manele
ree ster propeionstly
The ori any of sete Mom sper pales
ng Se was Tia pushed Wy Cay Mic 908 Mie
tik size excoeds A. Reasonably enough, Rayleigh Seating
isthe stall size ing eave ol Mie Seatering
large water droplets. tae same way. some mnenpsmive pla»
i fod conics and whe garage-bag past lok pale
ite light The garbage Bug iordr o be made pag
one oF the ed end othe
4.2.3 Transmission and the Index
of Refraction
a ongoing epeiise prensa watering and rain
Fach such even tac aphase shit inte igh fl
ich imately shows ap an a bit he apparent phase
That comenponds o an inde of tfraction forthe median
y = e or which cathe th nc ven ouh photos ei
Tosce hom hin comes aot return Fig 5 Rel
the scaler vet al combine o lane inthe onwards
‘Seton to form what might ox e alle the secondary
sur. Por empirical reasons one we con aici hat
Secondary wave will combine with what tothe prima
men mes propagate ron e
era old withthe perce the medium an ce
tainly poses an index of eration ers. There
a may appear to havea pase velo tes than qu
do. or ever rer ea The ew ti apparent oni
ti eid ts he Phase lationship between te second
‘ng me th primary diane ony ehe os
frequencies. Ax Me fequency ofthe cletomagncie ie
nc, he owas wi fa hd sen
heran as lg wil each OF ocres er
save the panivile_sharactexc ale. Problem &
phare pha ls fora dang ven car an Fi
13 sammie the est
{adn othe aps hn i ber fet ha must de
fen aaa ware el ap te oscil
Pers 49 Acne recrean cla anol
muay (ig 210) hy some amour han approximately A
and 180 ad u frequence above resonance lg anger
‘(8 ML Th much can be seen on gh side f Fig.
as overlap and, depending on their amplias and relative
Pas generat th net aramid dtrbance.Exsep forthe
La weakened hy seater paar wae aves
ina he terial Jos a itt were avening foe space. By
bre
Fire 4.10 soma war ad post secon nn
comparison 10 dis (re-space wave, which insted the
process the soul anse wave s phase shied and
pla irene is ech,
sun ranımied ware mus lo ig or cd) by one
amount Fg. A.) Th quai rhone wi er our
pores forthe moment ah té et en te
Pace ofthe resalta aho depends on the amples ofthe
muay (ig 210) hy some amour han approximately A
and 180 ad u frequence above resonance lg anger
‘(8 ML Th much can be seen on gh side f Fig.
as overlap and, depending on their amplias and relative
Pas generat th net aramid dtrbance.Exsep forthe
La weakened hy seater paar wae aves
ina he terial Jos a itt were avening foe space. By
bre
Fire 4.10 soma war ad post secon nn
comparison 10 dis (re-space wave, which insted the
process the soul anse wave s phase shied and
pla irene is ech,
sun ranımied ware mus lo ig or cd) by one
amount Fg. A.) Th quai rhone wi er our
pores forthe moment ah té et en te
Pace ofthe resalta aho depends on the amples ofthe
30 ar The Pasion oa
‘SHE alicia <a, Ihe secalry nl primary waves ae
‘utof phase hy 15 The
he refracted wane appris puc
‘ethene ware ace ra
ice in smite
Enemy. sac the sped of he wave the tof advance ol
amu ow fee pi vey To TS pe ie die
trance some pl Pay be wren a
phase shifts ich was ul up a the ware moved trough
vil eave any nd he equa nahe let wit
speed may der. Once aan, bul his tne m he medi ts
EAN an
where th sbtrastion off comesponds to a phase lg. An
ire a wl aveo wat a longer tie fora gnen re
(0 war in vacuum. That if you image mo paralle waves
‘he vacuum wave wi pas Pa time s/o before the other,
wave Cleary the. pare eg of er correspond
Fionn speed, and >t Sal. pla oa yield
process a continuous one, an the cumulative phase shit
Be 1 Ut patate he medium Tati wa. ea
He he conta ce Problem 4.9. In die sas major of sk
The Smportam exception i the case of X-ray propagan:
The oral frm nf, a depicted in Fig. 0
dex of the oscilfors and Irene ofthe secondary waves
the react wave lags ony slighty, and nie
‘The result isa gradually decreasing wave speed and an incrcas
‘SHE alicia <a, Ihe secalry nl primary waves ae
‘utof phase hy 15 The
he refracted wane appris puc
‘ethene ware ace ra
ice in smite
Enemy. sac the sped of he wave the tof advance ol
amu ow fee pi vey To TS pe ie die
trance some pl Pay be wren a
phase shifts ich was ul up a the ware moved trough
vil eave any nd he equa nahe let wit
speed may der. Once aan, bul his tne m he medi ts
EAN an
where th sbtrastion off comesponds to a phase lg. An
ire a wl aveo wat a longer tie fora gnen re
(0 war in vacuum. That if you image mo paralle waves
‘he vacuum wave wi pas Pa time s/o before the other,
wave Cleary the. pare eg of er correspond
Fionn speed, and >t Sal. pla oa yield
process a continuous one, an the cumulative phase shit
Be 1 Ut patate he medium Tati wa. ea
He he conta ce Problem 4.9. In die sas major of sk
The Smportam exception i the case of X-ray propagan:
The oral frm nf, a depicted in Fig. 0
dex of the oscilfors and Irene ofthe secondary waves
the react wave lags ony slighty, and nie
‘The result isa gradually decreasing wave speed and an incrcas
TABLE 41 Approximate Indices of Refraction
‘of Various Substances
AN equis as Pers e elie agape
ml: he antl wave ix nivancd in
nd ts speed exceeds c ta < 1) Ana inceate, the
ny duelo frequency dependent ss) in esciltor
molds and oi Aca higher egkence th se
cars waves, which now have very smal apie, Kad hy
3 The resin
Sigh phase, and
The precie shape of» paco nun) curve depends on
ihe speci oscilar damping as wells on the amount of
rancid waves advanced very
AS
sorption, ahıchm um depende on he numberof Oxi
os pricing
rigorous lin 1 propaga
problems know 36
43 facon 98
m crains dance anes gh
diese saspendn = c/n athe rm we. Hence
oh we shall simply asumo hat a hear propagating
‘through any sabrentive medina travels € a speed
Appart un quantum mechanical mel we cut
some Rave ae
Tht
casi done mathematical vis the expresion
able il ave
the concep of tela phase, Thus the index of refraction
farses when the absorption and emision process advances
‘retard the phases of te scattered photons, even as they
be infin it the theory
4.3 Reflection
ig ii
lei suchas. set of gan the wane et a 0
ose) Spaced toms hat some seater, Remember
(ne cas of anemic eg a ana ed, the sites
Ihe surface of taper
The note is an er
ange wo deren ranparent media such avi and las
enon reflection
eo ms radar te
10 that ofthe other over a distance of a wave.
Tengo more here wile very Ii rocio he morose
nh ke
Thies sory oly dominas change.
Hea, Rafecbon kom ec maten Am Ps, 80.1133
‘of Various Substances
AN equis as Pers e elie agape
ml: he antl wave ix nivancd in
nd ts speed exceeds c ta < 1) Ana inceate, the
ny duelo frequency dependent ss) in esciltor
molds and oi Aca higher egkence th se
cars waves, which now have very smal apie, Kad hy
3 The resin
Sigh phase, and
The precie shape of» paco nun) curve depends on
ihe speci oscilar damping as wells on the amount of
rancid waves advanced very
AS
sorption, ahıchm um depende on he numberof Oxi
os pricing
rigorous lin 1 propaga
problems know 36
43 facon 98
m crains dance anes gh
diese saspendn = c/n athe rm we. Hence
oh we shall simply asumo hat a hear propagating
‘through any sabrentive medina travels € a speed
Appart un quantum mechanical mel we cut
some Rave ae
Tht
casi done mathematical vis the expresion
able il ave
the concep of tela phase, Thus the index of refraction
farses when the absorption and emision process advances
‘retard the phases of te scattered photons, even as they
be infin it the theory
4.3 Reflection
ig ii
lei suchas. set of gan the wane et a 0
ose) Spaced toms hat some seater, Remember
(ne cas of anemic eg a ana ed, the sites
Ihe surface of taper
The note is an er
ange wo deren ranparent media such avi and las
enon reflection
eo ms radar te
10 that ofthe other over a distance of a wave.
Tengo more here wile very Ii rocio he morose
nh ke
Thies sory oly dominas change.
Hea, Rafecbon kom ec maten Am Ps, 80.1133
96 Chater Tee rapto oi
Internal and External Reflection
Imagine that ight is
Block of glas ig
heard in hal perpendicular o tc beam The two Semen
ren sepated, exposing he smooth al surfaces depicted
intig 125 Just before the cu was ade, there aso ht
wave cling he let inside the la we kno the beam,
nage Now there must hea nave (are) mss
{helo fect rom he surface ofthe ih hand lock. The
Implication sur accion of scatterers on and beneath the
“exposed surface ofthe right-hand Block is now "unpaired,
Cd. The region of les that was adjacent to hese pi
orto ec,
sumably also emir wavelet inthe backward diction that
were 107 outpace wth and cancel beam. Now they
Packs ar diction, an, in principle, each and evry mote
cle contribute othe reflected were Noves, m pc
tis, 4 4 a hin layer (=A/2 deep) of unpared atomic
clan nar he surface that i effectsly responsible or
thereleton, Foran r- pls interface, boat of he ene
Sit e releiedsrlgh ack vu by this er uf unpaired
Seauere(p 99, And that's tre wheter he lass LO rom
thik or 10m hick
Bean reflects off he ight hand Hock, und because ight
sus nally avi rom ls 1 amoo psa dens
nde ol inciden medium (7) sk than the index ofthe
ttasmiting medium Since am thing happens the
res hachwards Wi bea inciden perpndiclay it
isso at, 4% mus again be elected the tne as bal
2
> 4
Mr sch ges Bou pass a
feo ita sete back ose, Do fee bes cance
Tis process refered 2 Internal rfetin beans
ino Ifthe wo plas regions re made to approach one anocer
increasingly eos 10 tha we can imagine the pap 1 e à
th i of ay ar AOD) he elect igh wil is
‘i may sanishes a the mo faces merge and disp
rar andthe block Pecumesvoninuous again. Remember his
a relative phase shift between internally and external
reflected light tsee Sesion 4.1 for a more rigors rest
Experience withthe common mir makes obvios tur
ite ti rellested ie blue Tose
Sty, fin remember at he Layer ol scatterer esponnbe fr
he selection ete about Ahk as pr Fi.
“Thus the larger the wavelngth, the deeper the region con
the more settee thre ae acting together, Ticino ba
ance ou he fact that each seateer i ews efficient a À
args bse Po tte ned
Internal and External Reflection
Imagine that ight is
Block of glas ig
heard in hal perpendicular o tc beam The two Semen
ren sepated, exposing he smooth al surfaces depicted
intig 125 Just before the cu was ade, there aso ht
wave cling he let inside the la we kno the beam,
nage Now there must hea nave (are) mss
{helo fect rom he surface ofthe ih hand lock. The
Implication sur accion of scatterers on and beneath the
“exposed surface ofthe right-hand Block is now "unpaired,
Cd. The region of les that was adjacent to hese pi
orto ec,
sumably also emir wavelet inthe backward diction that
were 107 outpace wth and cancel beam. Now they
Packs ar diction, an, in principle, each and evry mote
cle contribute othe reflected were Noves, m pc
tis, 4 4 a hin layer (=A/2 deep) of unpared atomic
clan nar he surface that i effectsly responsible or
thereleton, Foran r- pls interface, boat of he ene
Sit e releiedsrlgh ack vu by this er uf unpaired
Seauere(p 99, And that's tre wheter he lass LO rom
thik or 10m hick
Bean reflects off he ight hand Hock, und because ight
sus nally avi rom ls 1 amoo psa dens
nde ol inciden medium (7) sk than the index ofthe
ttasmiting medium Since am thing happens the
res hachwards Wi bea inciden perpndiclay it
isso at, 4% mus again be elected the tne as bal
2
> 4
Mr sch ges Bou pass a
feo ita sete back ose, Do fee bes cance
Tis process refered 2 Internal rfetin beans
ino Ifthe wo plas regions re made to approach one anocer
increasingly eos 10 tha we can imagine the pap 1 e à
th i of ay ar AOD) he elect igh wil is
‘i may sanishes a the mo faces merge and disp
rar andthe block Pecumesvoninuous again. Remember his
a relative phase shift between internally and external
reflected light tsee Sesion 4.1 for a more rigors rest
Experience withthe common mir makes obvios tur
ite ti rellested ie blue Tose
Sty, fin remember at he Layer ol scatterer esponnbe fr
he selection ete about Ahk as pr Fi.
“Thus the larger the wavelngth, the deeper the region con
the more settee thre ae acting together, Ticino ba
ance ou he fact that each seateer i ews efficient a À
args bse Po tte ned
increases (remember 1/4. The combined real is that he
“face of à transparent medium reflects a wavelengths
‘out equally and doesn't appear colored in any way. Ts
== we wit se. ivy this page look white under ie
uma:
4.3.1 The Law of Reflection
Figure 4.13 shows a beam compose of plane waveons
inpinging at some anle on he smooth, at race afan opt
sally dense medium (et be glas. ASSUME tha The sr =
Hann ensionient is vacas Fale one vero
‘Ske of simplicity, in Figs 4.4 and 4.15 we have omited
erthin but one molecular layer atthe Interface, As the
vert descend Irene and renos one ae
ter another, each of which radiates a cam of photons
hat can be reparde sa heminperial wavelet inthe m
‘od, Because the wavelength so much greater than th
‘eyundon between the molecules, he wavelets emitted Back
inthe ince medium advance together and add cons
ively in only one direction, and thee is one well-defined
tected Yen, Tat would noe tu he incident radiation
te seaterer were far apar compared 10s they are fora
‘raion going (p46), in which case here woud also be
‘evo ected beans The direction o the lest beam
Fie 4.15 Teri da
phase dite
«e beoween the
angleotineidenee “
Fore AA A pare wore sus tire sos se Im Fig. 4.16, the ne AB ies long an incoming veto,
et Ten ast he rst ere eh ara she CD reson an ongoing sashrem etica, AB ans
“face of à transparent medium reflects a wavelengths
‘out equally and doesn't appear colored in any way. Ts
== we wit se. ivy this page look white under ie
uma:
4.3.1 The Law of Reflection
Figure 4.13 shows a beam compose of plane waveons
inpinging at some anle on he smooth, at race afan opt
sally dense medium (et be glas. ASSUME tha The sr =
Hann ensionient is vacas Fale one vero
‘Ske of simplicity, in Figs 4.4 and 4.15 we have omited
erthin but one molecular layer atthe Interface, As the
vert descend Irene and renos one ae
ter another, each of which radiates a cam of photons
hat can be reparde sa heminperial wavelet inthe m
‘od, Because the wavelength so much greater than th
‘eyundon between the molecules, he wavelets emitted Back
inthe ince medium advance together and add cons
ively in only one direction, and thee is one well-defined
tected Yen, Tat would noe tu he incident radiation
te seaterer were far apar compared 10s they are fora
‘raion going (p46), in which case here woud also be
‘evo ected beans The direction o the lest beam
Fie 4.15 Teri da
phase dite
«e beoween the
angleotineidenee “
Fore AA A pare wore sus tire sos se Im Fig. 4.16, the ne AB ies long an incoming veto,
et Ten ast he rst ere eh ara she CD reson an ongoing sashrem etica, AB ans
‘ar he wavelet mins rom A wll av at Cin-phase with
the wavelet just being emied fom D cas ti tml
ty Bas longs the dances AC nd BD are equal. note
wmode athe wavelets mins fom all he surface sane
es aro ave in-phase aed form a ile releuted plane
ave. t mist be tar AC = BD. Then, ios te wo ral
tive common hypotenuse
sing mu
wat
Ron thet othe tine Ar) ita for pot Bon
the waveltont o reach pont D on the surface the wave
mid rom A races poi C-In über wore, BD 4 =
AC, and so from the above equation ain 8, = in 8, which
meurt
o es
The anpl-ofincidence equals he angl-of reflection. This
uation he fis par of he Law of Reflection I intl,
appeared inthe book Catoprncs which was puporcdio hoe
Inn writen by Fi We say at a beam à normaly inc
dent when 8, = (Pin which exe 8, = 0° and fra mor e
beam eles buck on tel Similar, lance incidence cs
responds to 6, and perforce 8 = 97
Rays
Drawing waren can gel gS ca
Son OF ight The Imagery of anigiy was in terms e
Steg ie eas uz ht = notion ha or into Latin ss
ad andreschn nas royo A ray 1 ne dri
space corresponding tothe direction of flow of radiant ener
rar conser nat aplica emi.
Ameli a aniform homogeneou ay ae aight
‘he medi save inthe san gratin very direcion
‘hotope) the ra are perpendicular tothe mwavefrante
Tu dr a point source emiting spherical waves, the ey,
wich ae perpendicular fo them, point radial outward am
deso Staley ayas wäh pass waves ar
y daw oe incident ay and one elected ay (Fig 4.170).
All anges ar now measured rom the perpendicadar (o
the wavelet just being emied fom D cas ti tml
ty Bas longs the dances AC nd BD are equal. note
wmode athe wavelets mins fom all he surface sane
es aro ave in-phase aed form a ile releuted plane
ave. t mist be tar AC = BD. Then, ios te wo ral
tive common hypotenuse
sing mu
wat
Ron thet othe tine Ar) ita for pot Bon
the waveltont o reach pont D on the surface the wave
mid rom A races poi C-In über wore, BD 4 =
AC, and so from the above equation ain 8, = in 8, which
meurt
o es
The anpl-ofincidence equals he angl-of reflection. This
uation he fis par of he Law of Reflection I intl,
appeared inthe book Catoprncs which was puporcdio hoe
Inn writen by Fi We say at a beam à normaly inc
dent when 8, = (Pin which exe 8, = 0° and fra mor e
beam eles buck on tel Similar, lance incidence cs
responds to 6, and perforce 8 = 97
Rays
Drawing waren can gel gS ca
Son OF ight The Imagery of anigiy was in terms e
Steg ie eas uz ht = notion ha or into Latin ss
ad andreschn nas royo A ray 1 ne dri
space corresponding tothe direction of flow of radiant ener
rar conser nat aplica emi.
Ameli a aniform homogeneou ay ae aight
‘he medi save inthe san gratin very direcion
‘hotope) the ra are perpendicular tothe mwavefrante
Tu dr a point source emiting spherical waves, the ey,
wich ae perpendicular fo them, point radial outward am
deso Staley ayas wäh pass waves ar
y daw oe incident ay and one elected ay (Fig 4.170).
All anges ar now measured rom the perpendicadar (o
emite by millions upon millon of atoms wil combine 10
form single wel defined beam in process calle secu
reflection (rom the-word or a sammen minor ally
ancien times, speculum, Provided ie ides and valley are
Small compared to A, the setered wavelets wil sil ame.
more or les in pase whon @) 0, This i de sition
igre 4.17 1 Sec on ay ers beam on wars asada Figs 13.19, 416 snd. 17- One ater ad
She veloces Kan he anrcstckon te mess when the surface is rough in comparison o. aho the
bono peor dats ecg suo Dee nennen wl equal he angle ecto lor och
RES ee Sere We pre fr, Peo he oe ray vil emerge ete Which my, on
Sting hat alle diffe reflection (ee poo) Both
sural tothe surface, and and, have the same numerical
vales before Fig. 463,
ancient Grcksknew the Law of Refs
diced y observing the behavior of fat, and now
days that obseration can be Gone most imply witha Th
boon even ener inner acer The second po the
Law of Reflection minas th the incident ay the er
renier tothe surface, and the reflected ray alle na
Plane called she plane-oF incidence (Pi. + 1793 a
Are dimensional ies. Try 161 some target a mom
‘ha sli be by vellesting i off satlonar iro,
{the importance ofthis sesond par ofthe Law becomes
Sev
ing surface thats smooth cone for which any regular are fetpcon puc. The age buts io De Vale o be
soul compared to a wavelength) In tht cae. height reee
form single wel defined beam in process calle secu
reflection (rom the-word or a sammen minor ally
ancien times, speculum, Provided ie ides and valley are
Small compared to A, the setered wavelets wil sil ame.
more or les in pase whon @) 0, This i de sition
igre 4.17 1 Sec on ay ers beam on wars asada Figs 13.19, 416 snd. 17- One ater ad
She veloces Kan he anrcstckon te mess when the surface is rough in comparison o. aho the
bono peor dats ecg suo Dee nennen wl equal he angle ecto lor och
RES ee Sere We pre fr, Peo he oe ray vil emerge ete Which my, on
Sting hat alle diffe reflection (ee poo) Both
sural tothe surface, and and, have the same numerical
vales before Fig. 463,
ancient Grcksknew the Law of Refs
diced y observing the behavior of fat, and now
days that obseration can be Gone most imply witha Th
boon even ener inner acer The second po the
Law of Reflection minas th the incident ay the er
renier tothe surface, and the reflected ray alle na
Plane called she plane-oF incidence (Pi. + 1793 a
Are dimensional ies. Try 161 some target a mom
‘ha sli be by vellesting i off satlonar iro,
{the importance ofthis sesond par ofthe Law becomes
Sev
ing surface thats smooth cone for which any regular are fetpcon puc. The age buts io De Vale o be
soul compared to a wavelength) In tht cae. height reee
100 Captor neonato
auras Pes someuhere between them. Ths, allows the
pert ti page wae eier, marisco to he ar
aiesomewhere been ine and pela
4.4 Refraction
413 shows à beam of ight pinging on an erfae a
some angle (8, # 0) Te interacecoresponds o major
tot backward a the eflected eam, and forward, asthe
{tuned bean The fac vat he Incident rays ar ent oF
ured pu af their asa New pt, elle reas
sicily each energized molecule on the interface rites
recombine with Be unsetered remainder of the primary
ave. forthe netted wave. Te pe
‘over and ove gan she wave advances in he tan
rating medio, there is single nt ela single wet
‘ies esemally a6 the
slow wandten no he ga
Bates wih ante seed
ome atthe mera entered
ome back o thc imagen when we tale about Hoy ens
Principe ln any event, cane te coopentive phenomenon
‘own the wns eicomagnetie wave owe that
races pled turned Wit expect We acest
cinto. andthe foun Mens,
4.4.1 The Law of Refraction
Figure 419 picks up where we et off with Figs 4.13 and
4:16 The dira depit several av on, ll show aa
singe esti in time Remember tt each waveltot asar
{ace constant phe st the depres atthe ple 0e
auras Pes someuhere between them. Ths, allows the
pert ti page wae eier, marisco to he ar
aiesomewhere been ine and pela
4.4 Refraction
413 shows à beam of ight pinging on an erfae a
some angle (8, # 0) Te interacecoresponds o major
tot backward a the eflected eam, and forward, asthe
{tuned bean The fac vat he Incident rays ar ent oF
ured pu af their asa New pt, elle reas
sicily each energized molecule on the interface rites
recombine with Be unsetered remainder of the primary
ave. forthe netted wave. Te pe
‘over and ove gan she wave advances in he tan
rating medio, there is single nt ela single wet
‘ies esemally a6 the
slow wandten no he ga
Bates wih ante seed
ome atthe mera entered
ome back o thc imagen when we tale about Hoy ens
Principe ln any event, cane te coopentive phenomenon
‘own the wns eicomagnetie wave owe that
races pled turned Wit expect We acest
cinto. andthe foun Mens,
4.4.1 The Law of Refraction
Figure 419 picks up where we et off with Figs 4.13 and
4:16 The dira depit several av on, ll show aa
singe esti in time Remember tt each waveltot asar
{ace constant phe st the depres atthe ple 0e
act ied retarded by the tansmiting medium, cach wave
fro sed back, nt were, The wavefrons tend” as they
ros the boundary best ofthe speed change. Alemaive
‘je can envision Fi. 4.19 asanuileexponue pare of
ingle waveeon showing aller sccesive equal niemals
time. Notice ha inthe time A, which it takes fr pin 3
ona wavefront (raveling at spec 2) o reach point D. the
aie potion of hat same wavcron (easling a speed
ya rached point FH the ab (m
2 incident medium that 5 vacuum (n, =1) or ar (m)
be aveo bende The refracted wavefront extends fo &
SD making an angle wih be interface of @ As Beare. tie
io ingles ABD and AED it Fig. 4.19 share a common
Inptenase (D), and o
sin _ sin
wine HD = a rang AE = 9,30 Hence
sind ine
ipl bok sides by +, and since n, = c/o, and = <7,
Tri equation the is portion of he Law uf Refraction,
known ax Snell's Law alter the man who proposed 4
1621) Wilcbrord Snel Yan Royen (1591-1626. Snes
alse as boon lost bl contemporay accounts follow the
nent shown in Fig 4.2, What was found through obser
owas har bending o hey could equated wa
Sie
=
a
the ai to, which was constant fall, Tht constant
‘eas nly enough SANOS Me der refraction. eter
dir hats equivalent 0 Ea (4.4. We now know that be
Englishman Thomas Hantot had come wth same conclusion
before 1601. but he kept hiel
At fit, the indice of refraction were simply experien
tally determined constants ofthe psc sedi Later New
ton was actully ale fo derive Snell's Law using his own
peser teo. By ten e spicanceof a m
fe speed of em was evident Ste Shell's Law os
sown o be antral coonequene of Maxweils Elccromag
ete Theory (p12),
tis ada convenient to ransform the diagram no a ray
representation (Fig. 42) wherein al the anges are measured
from the perpendicular Along with E, (4), there goes the
understanding tht he incident, reflected and refracted rays
al iin the planeofinidence In the words the respec
tive unit propagation vectors and, ae coplanar i.
42
tin the lower inde medium, follows rom Sal's Law
atin > sn and ace he ane Fictions verre
positive between and 90" then > 8, Rater than gula,
fro sed back, nt were, The wavefrons tend” as they
ros the boundary best ofthe speed change. Alemaive
‘je can envision Fi. 4.19 asanuileexponue pare of
ingle waveeon showing aller sccesive equal niemals
time. Notice ha inthe time A, which it takes fr pin 3
ona wavefront (raveling at spec 2) o reach point D. the
aie potion of hat same wavcron (easling a speed
ya rached point FH the ab (m
2 incident medium that 5 vacuum (n, =1) or ar (m)
be aveo bende The refracted wavefront extends fo &
SD making an angle wih be interface of @ As Beare. tie
io ingles ABD and AED it Fig. 4.19 share a common
Inptenase (D), and o
sin _ sin
wine HD = a rang AE = 9,30 Hence
sind ine
ipl bok sides by +, and since n, = c/o, and = <7,
Tri equation the is portion of he Law uf Refraction,
known ax Snell's Law alter the man who proposed 4
1621) Wilcbrord Snel Yan Royen (1591-1626. Snes
alse as boon lost bl contemporay accounts follow the
nent shown in Fig 4.2, What was found through obser
owas har bending o hey could equated wa
Sie
=
a
the ai to, which was constant fall, Tht constant
‘eas nly enough SANOS Me der refraction. eter
dir hats equivalent 0 Ea (4.4. We now know that be
Englishman Thomas Hantot had come wth same conclusion
before 1601. but he kept hiel
At fit, the indice of refraction were simply experien
tally determined constants ofthe psc sedi Later New
ton was actully ale fo derive Snell's Law using his own
peser teo. By ten e spicanceof a m
fe speed of em was evident Ste Shell's Law os
sown o be antral coonequene of Maxweils Elccromag
ete Theory (p12),
tis ada convenient to ransform the diagram no a ray
representation (Fig. 42) wherein al the anges are measured
from the perpendicular Along with E, (4), there goes the
understanding tht he incident, reflected and refracted rays
al iin the planeofinidence In the words the respec
tive unit propagation vectors and, ae coplanar i.
42
tin the lower inde medium, follows rom Sal's Law
atin > sn and ace he ane Fictions verre
positive between and 90" then > 8, Rater than gula,
Fee 426
ur
(08 = men YG,
19 Uns pnt changes tate
Because the lading portion ofthe wavefront inthe glass
shows down the pat Lin he sir advances more randy
vaceping past and bending the wave toward the normal, (2)
Tae beatin the glass has a broader cross section than the
Tes the ar. nos, he tranamied energy I read hi
ter. 3) The wavelength decreases because the frequency is
inchaned while the speed decreases: A = o/ = e/nv and
a as
Tier notion sogesis hat he color spec of lg ie
‘thug ofa associated witht frequency or en. & =
do) han its wavelength, sine the wavelength changes with
‘he medium through wich the light moves. Coloris o much
physo-psychologial phenomenon (. 131 tat it must be
sate ginge, lee uh i sip
ta ed photons. When ve ak about vavelengts and coor.
se hou aaa be refering 0 vacuum wavelengthe
¡encon oe pen A)
Taal hesitation ree ths fart was assumed that he
ect and elected beams always had the sare frequency
as the incident beam, and that’s ordinaria reasonable
rg. Lip rg mio ona mn nd
motion That's cern the axe when the amplio oth
Vibration sar smal sis hen the electri el vig
bout 1000 V/m (tile the Bel i ess thas tenth of te
ans surface Mel), This st very large compare 10 the
Fields keeping a crystal together. which are ofthe oder of
10" V/m just about he same magnitude a he cote
fit holding te electon in a atom. We cas usualy expect
{he nca to vibrate in simple harmonic motion. and o
{he frequency will remain constant. the medium wil oc
‘acy respond incary That wll ot De rue, homer the
an be theca wih a igh: power laser So rive, at some
Aequeney + Wie mean can behave in nonlinear asia,
reveling ın reicenon and reactor ul harmonies Or. Se
«ic in ation to», Nowadays, second mone generates
(0. 681) are available commercial. You shine ed light
(6943 am) ito an appropriately rented transparent onli
etes (of for example. potassium dihydrogen posa
[RDP orammonium hydrogen phosphate ADP) and ou wil
‘One store of te above eat mes some fue ds
cuecion. It was reasonably assumed that each point on the
of the incident. reflected, and transmitted waves. In other
‘words eres a cd phase relationship between cach of the
ur
(08 = men YG,
19 Uns pnt changes tate
Because the lading portion ofthe wavefront inthe glass
shows down the pat Lin he sir advances more randy
vaceping past and bending the wave toward the normal, (2)
Tae beatin the glass has a broader cross section than the
Tes the ar. nos, he tranamied energy I read hi
ter. 3) The wavelength decreases because the frequency is
inchaned while the speed decreases: A = o/ = e/nv and
a as
Tier notion sogesis hat he color spec of lg ie
‘thug ofa associated witht frequency or en. & =
do) han its wavelength, sine the wavelength changes with
‘he medium through wich the light moves. Coloris o much
physo-psychologial phenomenon (. 131 tat it must be
sate ginge, lee uh i sip
ta ed photons. When ve ak about vavelengts and coor.
se hou aaa be refering 0 vacuum wavelengthe
¡encon oe pen A)
Taal hesitation ree ths fart was assumed that he
ect and elected beams always had the sare frequency
as the incident beam, and that’s ordinaria reasonable
rg. Lip rg mio ona mn nd
motion That's cern the axe when the amplio oth
Vibration sar smal sis hen the electri el vig
bout 1000 V/m (tile the Bel i ess thas tenth of te
ans surface Mel), This st very large compare 10 the
Fields keeping a crystal together. which are ofthe oder of
10" V/m just about he same magnitude a he cote
fit holding te electon in a atom. We cas usualy expect
{he nca to vibrate in simple harmonic motion. and o
{he frequency will remain constant. the medium wil oc
‘acy respond incary That wll ot De rue, homer the
an be theca wih a igh: power laser So rive, at some
Aequeney + Wie mean can behave in nonlinear asia,
reveling ın reicenon and reactor ul harmonies Or. Se
«ic in ation to», Nowadays, second mone generates
(0. 681) are available commercial. You shine ed light
(6943 am) ito an appropriately rented transparent onli
etes (of for example. potassium dihydrogen posa
[RDP orammonium hydrogen phosphate ADP) and ou wil
‘One store of te above eat mes some fue ds
cuecion. It was reasonably assumed that each point on the
of the incident. reflected, and transmitted waves. In other
‘words eres a cd phase relationship between cach of the
econ rs even pan incom
eme alo a point on fora conespondingrelted
no os nr contin an iw eid à
Tico, Sommer hs men at te asf re
{ane dred dec tom he eg of event
mech
4.4.2 Huygens’ Principle
Suppose a ight pases though nonurifonn sheet of gas,
wwe determine te eu fom 32 Or for that mater, what will
asin grin in 169 inthe work ene Trt del
1. ich had Bee write 12 yeas eatery he Dich
sicht Christian Huy ges tse hte hat he rice
ha ince Dee known a Huygens» Principe: vey
‘point on a propagaing wavefront seres as the source of
Spherical secondary wavelet, such thal the wavefront!
tome lter time fs the enelae of theve warez
"father erica point sat the propagating wave has
‘frequency », and is ranımined through he median ata
Speed 5, hen the secondary wavelet have that rae fe
‘gneney and send, Huygens wax bilan sin, and hk
Se ba eemarkably tht, tag gate nave
catering ery I's very erly etment a tater bas
‘ever shortcomings one of which is that st does ner
incorpora the coacept of interference and perforce Canos
Sul ith ral setering. Moreover the idea ta he sec
ondary wavelet propagate at speed determined by the medi
tam (a speed that may even Be anstropis eg. p 240) Ina
app ees. Nonetheless Huygens Principe can be usado,
are a Snes Law in away thats similar othe eames
that ed Eq. (Ad) Is probably best att fuse over the
psc dash a ondo ani propagation vac
2 151 Seah 1 Sen Am
Figwe 25 aot of porn ot
sn) und jus ws the Principle sa ool—a highly wef i
ter photons; he waves eee ae a heil
>
eme alo a point on fora conespondingrelted
no os nr contin an iw eid à
Tico, Sommer hs men at te asf re
{ane dred dec tom he eg of event
mech
4.4.2 Huygens’ Principle
Suppose a ight pases though nonurifonn sheet of gas,
wwe determine te eu fom 32 Or for that mater, what will
asin grin in 169 inthe work ene Trt del
1. ich had Bee write 12 yeas eatery he Dich
sicht Christian Huy ges tse hte hat he rice
ha ince Dee known a Huygens» Principe: vey
‘point on a propagaing wavefront seres as the source of
Spherical secondary wavelet, such thal the wavefront!
tome lter time fs the enelae of theve warez
"father erica point sat the propagating wave has
‘frequency », and is ranımined through he median ata
Speed 5, hen the secondary wavelet have that rae fe
‘gneney and send, Huygens wax bilan sin, and hk
Se ba eemarkably tht, tag gate nave
catering ery I's very erly etment a tater bas
‘ever shortcomings one of which is that st does ner
incorpora the coacept of interference and perforce Canos
Sul ith ral setering. Moreover the idea ta he sec
ondary wavelet propagate at speed determined by the medi
tam (a speed that may even Be anstropis eg. p 240) Ina
app ees. Nonetheless Huygens Principe can be usado,
are a Snes Law in away thats similar othe eames
that ed Eq. (Ad) Is probably best att fuse over the
psc dash a ondo ani propagation vac
2 151 Seah 1 Sen Am
Figwe 25 aot of porn ot
sn) und jus ws the Principle sa ool—a highly wef i
ter photons; he waves eee ae a heil
>
ge med homogeneous the sales pray He con
suet wi eal whereas i i OMEGA Ne
make this Fey clear, it shows a view of a wavefront 2. as
ellas numberof phen secondary wavelet, which, air
Somer ave propagated rad lo The crop of
advance wave Yi emy to vai th poses ferme
‘of mechanical vibration ofan cla metia, dee, te
(be as that Huygens envisioned it within the comen of
al prvading aer asc evident fom hi commen
Pancipl mathematically adding nthe concept of meter
Frewel Principe wa a diet cnsequence ofthe diferent
wre equation [Eq (60), therey puting ion im ath
‘ematical bas, Thal there was 3 nnd Tor refomulatio o
sl dex hemispherical wavelets Had we dran thers a
‘Ge sore something that snot observed Since Uist
oll we ned ot he it y à
44.3 Light Rays and Normal Congruence
pastis, one an pode wey ma feu emis of
Tate. a scream) and we might imagino any 4 he Ce
tial ito eramos of uch bam. ear
ne the sarc al directions) rays are orthogonal rajeciories
of the weft. That in sy, are
‘gona every point finersccnon Eves mc
anar is parle the propagation vector As yor
vs sap mural rss wl be singen, se by
Symmetry they cannot bend in amy preferred directo, ere
Being none. Moreover, because he speed o propagan
separation between two wavelons, mewsursd one 193,
intersects a set of wavefronts are called corresponding pos
fee example AA" and a" in Fig 427. Baden, she pur
formed into 3” aftr a me”, the distance betwsen core
sponding point on any and al ray wll be averse in that
fom one homogeneousetrpie medi ito ante. This
jus mean ht ech point on 2 can be imagined following
the path ary tone st in the time
h of them, they are si 0
svthogona o cach and every
fiom a point source are perpendicular 104 sphere centered at
‘We can on tie considera scheme that wll alo alow
sto fallow the progress of ig trough various tropic
media. The haw for thie apre she Theorem of Malen
{and Dupin itodaced 1 108 hy F Mal end modif in
euch
suet wi eal whereas i i OMEGA Ne
make this Fey clear, it shows a view of a wavefront 2. as
ellas numberof phen secondary wavelet, which, air
Somer ave propagated rad lo The crop of
advance wave Yi emy to vai th poses ferme
‘of mechanical vibration ofan cla metia, dee, te
(be as that Huygens envisioned it within the comen of
al prvading aer asc evident fom hi commen
Pancipl mathematically adding nthe concept of meter
Frewel Principe wa a diet cnsequence ofthe diferent
wre equation [Eq (60), therey puting ion im ath
‘ematical bas, Thal there was 3 nnd Tor refomulatio o
sl dex hemispherical wavelets Had we dran thers a
‘Ge sore something that snot observed Since Uist
oll we ned ot he it y à
44.3 Light Rays and Normal Congruence
pastis, one an pode wey ma feu emis of
Tate. a scream) and we might imagino any 4 he Ce
tial ito eramos of uch bam. ear
ne the sarc al directions) rays are orthogonal rajeciories
of the weft. That in sy, are
‘gona every point finersccnon Eves mc
anar is parle the propagation vector As yor
vs sap mural rss wl be singen, se by
Symmetry they cannot bend in amy preferred directo, ere
Being none. Moreover, because he speed o propagan
separation between two wavelons, mewsursd one 193,
intersects a set of wavefronts are called corresponding pos
fee example AA" and a" in Fig 427. Baden, she pur
formed into 3” aftr a me”, the distance betwsen core
sponding point on any and al ray wll be averse in that
fom one homogeneousetrpie medi ito ante. This
jus mean ht ech point on 2 can be imagined following
the path ary tone st in the time
h of them, they are si 0
svthogona o cach and every
fiom a point source are perpendicular 104 sphere centered at
‘We can on tie considera scheme that wll alo alow
sto fallow the progress of ig trough various tropic
media. The haw for thie apre she Theorem of Malen
{and Dupin itodaced 1 108 hy F Mal end modif in
euch
ere 428 Winn oa fonte suc Se es
1616 by C. Dupin), according to which group ef rays wil
preserve its normal congruence afer any number of reflec
Tins and refractions as in Fig 427), From our presen van
sement ¡hal say remain orthogonal Lo wavelrons throug
‘all propagation processes in etropic medi, AS shown in
Problem 425, the theoren can e ud to derive the Law of
Rein se el Sres Law. I I often mos comenten
10 cary ud a ray trace though an oplical ystems ad then
reset the wavefronts wing the ea of equal rat ies
4.5 Fermat's Principle
in which ight propagates in general: can be vice (rom a
‘entirely differnt and intriguing perspective afforded us by
Fermat's Principe The ess ha wil ufo presen hse
‘hough aná beyond th say of Clasica Opus
Alexandria, who lived some ime
Si) 9. amd x0. 250, wate fro props
Hero o
rave a a het“ lavan. Presamaby only ne
ofthese paths wil have any physical alt. If we dew he
SBP ete) But obviously the siught ine path BF.
‘whch correspond to = 8,1 shorts posible on. The
Same hind of reasoning Problem 431) make viet a
pois and Peas iin what hs previusly ben defined
2 Ihe plane-ob incidence. For over Ten hundred years
observation sos alone, uni in 1657 Term
"compass both flection and re
Aer an inerface des not ake sight neo ie
‘petal ph betwen plain incide medium and one in
‘he vasmiting medium. Far consequeny reformular
He's stement to ea the actual path benieen nu point
time. As we shal sc. even this frm ofthe statement i
complete and a ira a For the moment DE
le us embrace bt no peso
action. A beam of Hight
Se
Fine 429 Ferma Pace apie to ret
1616 by C. Dupin), according to which group ef rays wil
preserve its normal congruence afer any number of reflec
Tins and refractions as in Fig 427), From our presen van
sement ¡hal say remain orthogonal Lo wavelrons throug
‘all propagation processes in etropic medi, AS shown in
Problem 425, the theoren can e ud to derive the Law of
Rein se el Sres Law. I I often mos comenten
10 cary ud a ray trace though an oplical ystems ad then
reset the wavefronts wing the ea of equal rat ies
4.5 Fermat's Principle
in which ight propagates in general: can be vice (rom a
‘entirely differnt and intriguing perspective afforded us by
Fermat's Principe The ess ha wil ufo presen hse
‘hough aná beyond th say of Clasica Opus
Alexandria, who lived some ime
Si) 9. amd x0. 250, wate fro props
Hero o
rave a a het“ lavan. Presamaby only ne
ofthese paths wil have any physical alt. If we dew he
SBP ete) But obviously the siught ine path BF.
‘whch correspond to = 8,1 shorts posible on. The
Same hind of reasoning Problem 431) make viet a
pois and Peas iin what hs previusly ben defined
2 Ihe plane-ob incidence. For over Ten hundred years
observation sos alone, uni in 1657 Term
"compass both flection and re
Aer an inerface des not ake sight neo ie
‘petal ph betwen plain incide medium and one in
‘he vasmiting medium. Far consequeny reformular
He's stement to ea the actual path benieen nu point
time. As we shal sc. even this frm ofthe statement i
complete and a ira a For the moment DE
le us embrace bt no peso
action. A beam of Hight
Se
Fine 429 Ferma Pace apie to ret
Avan example of he application ofthe pine tothe ce
refrain, ler to Fig 429, where we minimizan
"time from St P with respect othe arabe x ln other
ro changing si pont O changing ray rom So P
The smallest transit me will then resumablycoicie wih
sa path Hence
To mimi 10) with respect 10 vaa in we set
Hi = ati
ET ET DAT EN ae
‘ang he diagram, we con rewrite he expresion a
sino
sis oles than Sel Law (Fa. 44) Wa beam of ight
sance rom 10 P I Ihe eas OSSD Um. It must
‘py wih the aw of Refraction
‘Stppose tha we have asralifid atrial composed of
ayer ach having a ferent index of refraction, a in Fi
450 Mean ie from So Pil hen be
re and , ae the pat length and speed respectively
15 ms a»
le nicht mation is known a th optical path length
¡OPE rene by the ay. contas tot «ara! path
eg 3 Clery foran inhomogeneous mec where
sauna of postion, the summation must be changed to
enel
Fiera 30 à
suivant he distance tard) in he ei of index
ir Thats tbe two wil correspon tothe same number o
avelegts, (OP) A0 = 5, ad ho sume phase change a
The ight advances.
ple: igh in going from point Sto P.raverse the roue ar
ing the males optical path lena
Format and Mirages
Wien light a fom the Sun pass though the inhomoge-
neous atmosphere of the Earth a show I ig. 5.31. ty
tend soa to rave the lower, deme regions a abruptly =
Fire 431. he dng fy roi vomogi meda.
snare
refrain, ler to Fig 429, where we minimizan
"time from St P with respect othe arabe x ln other
ro changing si pont O changing ray rom So P
The smallest transit me will then resumablycoicie wih
sa path Hence
To mimi 10) with respect 10 vaa in we set
Hi = ati
ET ET DAT EN ae
‘ang he diagram, we con rewrite he expresion a
sino
sis oles than Sel Law (Fa. 44) Wa beam of ight
sance rom 10 P I Ihe eas OSSD Um. It must
‘py wih the aw of Refraction
‘Stppose tha we have asralifid atrial composed of
ayer ach having a ferent index of refraction, a in Fi
450 Mean ie from So Pil hen be
re and , ae the pat length and speed respectively
15 ms a»
le nicht mation is known a th optical path length
¡OPE rene by the ay. contas tot «ara! path
eg 3 Clery foran inhomogeneous mec where
sauna of postion, the summation must be changed to
enel
Fiera 30 à
suivant he distance tard) in he ei of index
ir Thats tbe two wil correspon tothe same number o
avelegts, (OP) A0 = 5, ad ho sume phase change a
The ight advances.
ple: igh in going from point Sto P.raverse the roue ar
ing the males optical path lena
Format and Mirages
Wien light a fom the Sun pass though the inhomoge-
neous atmosphere of the Earth a show I ig. 5.31. ty
tend soa to rave the lower, deme regions a abruptly =
Fire 431. he dng fy roi vomogi meda.
snare
Fear 4.32 er bo nest corto
pose, mining the OP. Ego, ne con til se the Sun
no same way. ond viewed a glancing angle as in
Fig 4.39, appears to eft the environs on if it were covered
with shoe of war. The ur cathe roadway is warmer und
renal by Gladstone and Dale tat fora gas of den »
wer
ANS om te Hea Gis Law tata fe pressure,
since p= P/E, = 1) Late bter the 0, the lower
And of relation of he ar immedieh above
he 1 heading somes enr woul aks arte
ttatmininized the PL, Suh ray woul bend uprard, pas
ing dosh mor of the les dens ar than had veld
sgh To apreit hw tht mor, imagine the ar id
inte ining number ninia thin coman
end via Stel’ Lomo slighty upward at each werace
‘wards), OF course ifthe ray comes down nealy vertically i
ayer. ony bends sigh! and soon ses he round where
‘On the other hand, its posible that a igh ry that comes
approach an terface at glancing. incidence (p.116). I woukl
‘limb back up ito the more deme air (much in Fig 29
‘Any viewer, fon thet in Fig 4.2, who receives thet
enc rays natal projets he ph ack asi they
see riet fons mond srface, Depending on wher
you Hand, yo’ se a different mirage pole, ut wil
aay far from you and o will aways disappenr as yon
Approach it The effec i paiculary easy to vw on ong
modem High. The oly requirements at ook at ie
IE
Figura 430 De ui cag ca be er
en
pose, mining the OP. Ego, ne con til se the Sun
no same way. ond viewed a glancing angle as in
Fig 4.39, appears to eft the environs on if it were covered
with shoe of war. The ur cathe roadway is warmer und
renal by Gladstone and Dale tat fora gas of den »
wer
ANS om te Hea Gis Law tata fe pressure,
since p= P/E, = 1) Late bter the 0, the lower
And of relation of he ar immedieh above
he 1 heading somes enr woul aks arte
ttatmininized the PL, Suh ray woul bend uprard, pas
ing dosh mor of the les dens ar than had veld
sgh To apreit hw tht mor, imagine the ar id
inte ining number ninia thin coman
end via Stel’ Lomo slighty upward at each werace
‘wards), OF course ifthe ray comes down nealy vertically i
ayer. ony bends sigh! and soon ses he round where
‘On the other hand, its posible that a igh ry that comes
approach an terface at glancing. incidence (p.116). I woukl
‘limb back up ito the more deme air (much in Fig 29
‘Any viewer, fon thet in Fig 4.2, who receives thet
enc rays natal projets he ph ack asi they
see riet fons mond srface, Depending on wher
you Hand, yo’ se a different mirage pole, ut wil
aay far from you and o will aways disappenr as yon
Approach it The effec i paiculary easy to vw on ong
modem High. The oly requirements at ook at ie
IE
Figura 430 De ui cag ca be er
en
Men lio sel en piton Fe
The wavefronts end because of temperature induced changes
‘speed and herefore in watelength. (The speed o sound is
optional othe quate 1001 Fe temperature) The noses
people n a hot beach limbup nd aay and the plac an
semstrangely quie, The opposite curs in he evening when
he round co before he upper air and distant sounds can
The Modern Formulation of Fermat's Principle
Tieoriinl teen of Fermat's Principle of Laat Tm hs
me seis falling nd in nee of eration, To hat end
wcll buf we ive function. say ji. We on determine the
gs value ofthe variable tht causes fx) wo have at
‘inary value by sting fd = Osa elving for By asta
mary vale, we mean one for which he slope of i) versa
Tis ae or Svan where Uh faction has a mati
- fora point fiction with à horizontal.
Fermat Principe is wider fre rd ih ry im
sein frm point Se point P mat averse an optical path
length thas saionary with respect to variations ofthat
th In essence what that means is at the curve of the OPL
“esi. will aves somewhat atened region in he Wiciniy
tere the slope goes o ero. The voto ope point come
‘pom to the actual path taken. In other words the OPL for
Sete wajetry wil equal to it approximation the OPL
tf pats immediately adjacent wo i. For example ina stu
an vr the OPL sa minero, a withthe refrain ls
tated in Fig 429. the OP: curve wil lok something like
# ere 434 toe su
“Test dea oe PL ate s Tay ses non,
Fig. 4:34. A small change in x in he vicinity nf 0 as ile
effect onthe UPL, bala similar change in y ampuher wei
away rom 0 cess in aubstatial change in OPL- Thus
there wil he ray path neighboring the scl one tht woul
{ake early the sme time forthe ight to tras, This ster
insight makes it possible o begin to understand how ish
‘manages to be so clever init meandeings.
"Suppen tat ncam of neh anes rang a oo
neous isotropic medium (Fig 435) so a ara pas rem
Posto P Atoms within the material ae drive y the ne
et distrbance, andtheyreradists in all iections. Wavelets
progresin along path te immediate vicinity ofa station
iy straight-line path will each 7 toate at differ ony
Slightly OPL (as with group. in Fig. 4359), The will
therefore amive nearly in-pase and reinforce each other.
Think ofeach wavelet represented by ny phasor hat ote
once around u Ihe wave advances one wavelength (23)
long an ry path, Because he OPÍS ars al about the sae,
the phasors a al point in more oros the same direction.
and even though they" al small hey combine to make the
dominant contbuton
Wavelets aking other país fr fom the stationary one (as
‘ith group Fig 4350) will rivet P appreciably out
phase with each other and wil therefore tend to cancel. Tooth
E>A
The wavefronts end because of temperature induced changes
‘speed and herefore in watelength. (The speed o sound is
optional othe quate 1001 Fe temperature) The noses
people n a hot beach limbup nd aay and the plac an
semstrangely quie, The opposite curs in he evening when
he round co before he upper air and distant sounds can
The Modern Formulation of Fermat's Principle
Tieoriinl teen of Fermat's Principle of Laat Tm hs
me seis falling nd in nee of eration, To hat end
wcll buf we ive function. say ji. We on determine the
gs value ofthe variable tht causes fx) wo have at
‘inary value by sting fd = Osa elving for By asta
mary vale, we mean one for which he slope of i) versa
Tis ae or Svan where Uh faction has a mati
- fora point fiction with à horizontal.
Fermat Principe is wider fre rd ih ry im
sein frm point Se point P mat averse an optical path
length thas saionary with respect to variations ofthat
th In essence what that means is at the curve of the OPL
“esi. will aves somewhat atened region in he Wiciniy
tere the slope goes o ero. The voto ope point come
‘pom to the actual path taken. In other words the OPL for
Sete wajetry wil equal to it approximation the OPL
tf pats immediately adjacent wo i. For example ina stu
an vr the OPL sa minero, a withthe refrain ls
tated in Fig 429. the OP: curve wil lok something like
# ere 434 toe su
“Test dea oe PL ate s Tay ses non,
Fig. 4:34. A small change in x in he vicinity nf 0 as ile
effect onthe UPL, bala similar change in y ampuher wei
away rom 0 cess in aubstatial change in OPL- Thus
there wil he ray path neighboring the scl one tht woul
{ake early the sme time forthe ight to tras, This ster
insight makes it possible o begin to understand how ish
‘manages to be so clever init meandeings.
"Suppen tat ncam of neh anes rang a oo
neous isotropic medium (Fig 435) so a ara pas rem
Posto P Atoms within the material ae drive y the ne
et distrbance, andtheyreradists in all iections. Wavelets
progresin along path te immediate vicinity ofa station
iy straight-line path will each 7 toate at differ ony
Slightly OPL (as with group. in Fig. 4359), The will
therefore amive nearly in-pase and reinforce each other.
Think ofeach wavelet represented by ny phasor hat ote
once around u Ihe wave advances one wavelength (23)
long an ry path, Because he OPÍS ars al about the sae,
the phasors a al point in more oros the same direction.
and even though they" al small hey combine to make the
dominant contbuton
Wavelets aking other país fr fom the stationary one (as
‘ith group Fig 4350) will rivet P appreciably out
phase with each other and wil therefore tend to cancel. Tooth
E>A
110 Chapter & the Prato lL
ao
a a ca
A ae
‘We am expect ht his sae logic hd fr propagation
rocesen® nich an, for example election from Pane
Mar (Fig. 4.28). There, spherical wave leaving ace
row the etre ior, yet an observe at P wees 3 well
defined pin source and nt à great loch of ight ovins
nig 436) have the ace wavelets
‘il ave ven in pave und rior each tes. A
‘fier ays eg groso in Fig 4.36) wll mike nego
Stationary Paths
dimensional ei idal itor. the source Sand the obser
Tength SOP willbe conan. regacics of where on de
primate happens I be tis alo a geometria propery a
the clipe du — 8, or ny location oF QA pic! pl
{tom $ o Pi recio ar therefore precise equal Nowe
bu minimum. andthe OPI. i early tatonary wth espe
athe focus? From anther viewpoint we can sy hat ai
red srlace such that the waves will tata ré
ore ah ter only al P whee they have veld the se
sistance and have the same phase. In any cae, plane mi
ror wis angen wth elie a the exact are pa SOP
traversed by aray would then be alive minimum. Atte
tying thin the elipse he ved one shown thats
Ths me eve hough oer used ph uber 8 + 4
Fs) Tha a cave he ys roel storey OL
Sv tbe Pile peaks only abot he pat ad ae
tone arene Don STE TT vy ta gt
ema’ achievement stimulated grea elf ef o
{ima online werk of many nun nad Poe
de cha ofp tans Lange (36 NL a
rowan Hanilon «18 1169). The sig. milan
Vapor par la Shige decopmen of Qu.
Seal Quarante an nl
ao
a a ca
A ae
‘We am expect ht his sae logic hd fr propagation
rocesen® nich an, for example election from Pane
Mar (Fig. 4.28). There, spherical wave leaving ace
row the etre ior, yet an observe at P wees 3 well
defined pin source and nt à great loch of ight ovins
nig 436) have the ace wavelets
‘il ave ven in pave und rior each tes. A
‘fier ays eg groso in Fig 4.36) wll mike nego
Stationary Paths
dimensional ei idal itor. the source Sand the obser
Tength SOP willbe conan. regacics of where on de
primate happens I be tis alo a geometria propery a
the clipe du — 8, or ny location oF QA pic! pl
{tom $ o Pi recio ar therefore precise equal Nowe
bu minimum. andthe OPI. i early tatonary wth espe
athe focus? From anther viewpoint we can sy hat ai
red srlace such that the waves will tata ré
ore ah ter only al P whee they have veld the se
sistance and have the same phase. In any cae, plane mi
ror wis angen wth elie a the exact are pa SOP
traversed by aray would then be alive minimum. Atte
tying thin the elipse he ved one shown thats
Ths me eve hough oer used ph uber 8 + 4
Fs) Tha a cave he ys roel storey OL
Sv tbe Pile peaks only abot he pat ad ae
tone arene Don STE TT vy ta gt
ema’ achievement stimulated grea elf ef o
{ima online werk of many nun nad Poe
de cha ofp tans Lange (36 NL a
rowan Hanilon «18 1169). The sig. milan
Vapor par la Shige decopmen of Qu.
Seal Quarante an nl
ode tomalis of Quantum Opt si
A wil yield night under a myrad of circumstances.
4.6 The Electromagnetic Appro
Tut ar we have died reflection and eration fom te
pertes lSestein Theory, the Theor! Maks ad
Duplo, and Fermat's Principle. Yet naher and even more
Unit previous totes. which ay nothing ab he
inciden rece, and rami radiant ax dense he
Fo le sepocively) Elecomagneic Theory tests thee
ork of ar more complete desenptin,
4.6.1 Waves at an Interface
o Mani hs he form
E.= En cos dE 0 a
ox plane polarize We din Chapter Sar any oma
light an be reprend by two ontbogonl lines placed
he rin O in space, whee F = 0. Thus making no asump
or amplitude, we can wit the flected and raat
hr un
=u ee duced becas the postion o the origin o unique iure
Cer nen re A M depict the verses in the ven of the planar interface
A wil yield night under a myrad of circumstances.
4.6 The Electromagnetic Appro
Tut ar we have died reflection and eration fom te
pertes lSestein Theory, the Theor! Maks ad
Duplo, and Fermat's Principle. Yet naher and even more
Unit previous totes. which ay nothing ab he
inciden rece, and rami radiant ax dense he
Fo le sepocively) Elecomagneic Theory tests thee
ork of ar more complete desenptin,
4.6.1 Waves at an Interface
o Mani hs he form
E.= En cos dE 0 a
ox plane polarize We din Chapter Sar any oma
light an be reprend by two ontbogonl lines placed
he rin O in space, whee F = 0. Thus making no asump
or amplitude, we can wit the flected and raat
hr un
=u ee duced becas the postion o the origin o unique iure
Cer nen re A M depict the verses in the ven of the planar interface
Fire 4.38 Pare wns cert nt cay ea e
“The laws of lecromagne Theory (Section 3.) end 45
sagen tt tenet ye es. hy
{theses thatthe component of the elect eld E that isan
sen the interface must be continous cross (he same e
te fr Hn other words ih total angen component of
E on one side ofthe surface must equal that onthe other
(Problem 437) Tas, ce isthe uni veto noma The
Interac, regardless o the ici ofthe elects eld with
inthe watt, the cov-produt of wth O, wll be per
pendu to, an therefore tungen the etree Hence
EL]
6, x Ecos top
+O, xB cos Fos te)
G, XE, cose wr Fay ws
“The relations mast obi at any insta in tim and at any
soi om te interface (x = 5), Consequently, E, E, and E
mus have precise} te ame Tuncionl dependence on the
Variables and, ich means that
Maa
dio
APA
‘an expresion independent ol and , as indeed must be.
Toss as his us 0 De ue for ll ales of ime the sot
les of rest be equal 0 wit
Recall thatthe cecrons within the medi are undergoing (i
A o UE + a A)
{elton fo be vai epudless ot location (For example
{he origin might be chosen such that F was erpendcular À
tanto ork) Hom the first wo terms Obs
Recaling Eq (2.43), this expresion simply sys thal the et
pit of seeps ou plane (whic is of esse te intra
perpenicala i tie velr R, = K). To phrase A il i
Tere = Ris pare à, Novice weve, at ee
the menden and elected a are an es mcm &
KL From te fact that ky — E) Js ng component in the pane
ofthe trac, ha, Dax By) =O, we cone ht
sin kn,
ence we have the Lan of Rhin thas
ane
Bunhermore since Æ, — Ey is parallel 4, al ee veut,
À. and à, ar in the same plane, e plane-ot incidence.
Ain om Ea 79)
TEA au
and therefore, ~ Rp also normal tothe interface, Ts
kE. an à, ar al coplanar. As before, the tangential com
‘ponents Fk and must be equal and coment
ain = sin [ee
But cause = a,
wean muliply both sides by c/o
mn 0 = sia 8
‘whichis Snes Law Fal we ad hos the ri 70
“The laws of lecromagne Theory (Section 3.) end 45
sagen tt tenet ye es. hy
{theses thatthe component of the elect eld E that isan
sen the interface must be continous cross (he same e
te fr Hn other words ih total angen component of
E on one side ofthe surface must equal that onthe other
(Problem 437) Tas, ce isthe uni veto noma The
Interac, regardless o the ici ofthe elects eld with
inthe watt, the cov-produt of wth O, wll be per
pendu to, an therefore tungen the etree Hence
EL]
6, x Ecos top
+O, xB cos Fos te)
G, XE, cose wr Fay ws
“The relations mast obi at any insta in tim and at any
soi om te interface (x = 5), Consequently, E, E, and E
mus have precise} te ame Tuncionl dependence on the
Variables and, ich means that
Maa
dio
APA
‘an expresion independent ol and , as indeed must be.
Toss as his us 0 De ue for ll ales of ime the sot
les of rest be equal 0 wit
Recall thatthe cecrons within the medi are undergoing (i
A o UE + a A)
{elton fo be vai epudless ot location (For example
{he origin might be chosen such that F was erpendcular À
tanto ork) Hom the first wo terms Obs
Recaling Eq (2.43), this expresion simply sys thal the et
pit of seeps ou plane (whic is of esse te intra
perpenicala i tie velr R, = K). To phrase A il i
Tere = Ris pare à, Novice weve, at ee
the menden and elected a are an es mcm &
KL From te fact that ky — E) Js ng component in the pane
ofthe trac, ha, Dax By) =O, we cone ht
sin kn,
ence we have the Lan of Rhin thas
ane
Bunhermore since Æ, — Ey is parallel 4, al ee veut,
À. and à, ar in the same plane, e plane-ot incidence.
Ain om Ea 79)
TEA au
and therefore, ~ Rp also normal tothe interface, Ts
kE. an à, ar al coplanar. As before, the tangential com
‘ponents Fk and must be equal and coment
ain = sin [ee
But cause = a,
wean muliply both sides by c/o
mn 0 = sia 8
‘whichis Snes Law Fal we ad hos the ri 70
‘wine arose, is evident rom Ep. 820) and 4.21)
tate and , would both have been zero. That arangement
hough na inch, is crtäiny per. ad we'l set
46.2 The Fresnel Equations
We ave jus found te relationship that eis among the
sea (7.0, BF and Fats boundary There
Dail an interdependence shared bythe amplis Ey, Es
and. which ean now be evaluate To that end suppose
fat plane ona ave set on thin
‘ecsearating eo stop medi. Whatever the poliza
he ave la Em cle no compe
et para and perpedicna to the plan 0 incidence and
ue E perpendicular to the lane-inciece. Assure
A is perpendicular tot plane-oF inciden aná at Bis
sel oi Fig, 49) Recal at = 08 tat
Ea any
RE=0 42
‘cB. and the uni propagation veto form aight and
‘em, Apsin, making use of fe connut of the angen
dans pint,
enn relly ought to be cevsioned ty =O tie, atthe sor
i) om which te) have Been displce forthe sake of
le Not oo hat though and ust noma othe
ine atancitence By syne are uessng tha hes
pu sand at he ete when E, does. The directions of
de E als then follow fom Ea. (323)
‘We il need to invoke air o 1e boundary condi
order to ge on more equation. Th presence of materia
cc at become cletcallypoavized by the wave has
sii fet onthe eld conne Ths, hough e
Inga componen of Eis ont arse ie bound.
‘mal components nt. nse he nomma component of
Se odres o same on either side of the iras, Sim
>
“ 4 =
oN
lay he nora component of i continuous, asthe tu
set sompenent of Here the maga effet he
our condition wil be the simples to une. parlar as
appli reichen fom te srface of conductor * Te
a
sa
Be sn = =,
‘where the left and ight sides are he oa magnitudes of Hy.
Pall te intrave inthe incident and transiting media
‘espetively The postive ection ita of increasing. o
ag nh te un ey Eng Bad at
tate and , would both have been zero. That arangement
hough na inch, is crtäiny per. ad we'l set
46.2 The Fresnel Equations
We ave jus found te relationship that eis among the
sea (7.0, BF and Fats boundary There
Dail an interdependence shared bythe amplis Ey, Es
and. which ean now be evaluate To that end suppose
fat plane ona ave set on thin
‘ecsearating eo stop medi. Whatever the poliza
he ave la Em cle no compe
et para and perpedicna to the plan 0 incidence and
ue E perpendicular to the lane-inciece. Assure
A is perpendicular tot plane-oF inciden aná at Bis
sel oi Fig, 49) Recal at = 08 tat
Ea any
RE=0 42
‘cB. and the uni propagation veto form aight and
‘em, Apsin, making use of fe connut of the angen
dans pint,
enn relly ought to be cevsioned ty =O tie, atthe sor
i) om which te) have Been displce forthe sake of
le Not oo hat though and ust noma othe
ine atancitence By syne are uessng tha hes
pu sand at he ete when E, does. The directions of
de E als then follow fom Ea. (323)
‘We il need to invoke air o 1e boundary condi
order to ge on more equation. Th presence of materia
cc at become cletcallypoavized by the wave has
sii fet onthe eld conne Ths, hough e
Inga componen of Eis ont arse ie bound.
‘mal components nt. nse he nomma component of
Se odres o same on either side of the iras, Sim
>
“ 4 =
oN
lay he nora component of i continuous, asthe tu
set sompenent of Here the maga effet he
our condition wil be the simples to une. parlar as
appli reichen fom te srface of conductor * Te
a
sa
Be sn = =,
‘where the left and ight sides are he oa magnitudes of Hy.
Pall te intrave inthe incident and transiting media
‘espetively The postive ection ita of increasing. o
ag nh te un ey Eng Bad at
that he salar components of and B, appear wih minus
Sens rom 142 hve
B= Edo, amy
Since = ant = 0,4. (32610 rien as
‘ng that the cones hein equal one another af =O, we
rs = Face een am
Combines wt Eg (125), ti
M os = Mo
a
and (ke) m 433)
The Lub serves a a reminder hat we ate desing with
theca in hich Eis peypendculrt he plane-aincidence
These uo expressions, hic are com
e 10 ofthe Fresnel Equation. Mos ofen one del with
dcksice or vt =
form of tes equations is simply
o: conque, he com
(fie) 15060 meosa 439
A ET
ete denotes the mpd recon cuca
iste tpl envi tie
Cae 2: para tthe plane obinidence in pie
the plane-oFncdence ax shown in Fig 440, Continuity
the tungen components of Fon che side ofthe bound,
Prend # re
ray e before onto ofthe tanger
ie elds
component of
Using he fer ha = ad = ewe an combi
Beas = "eos
NE | case + con =
Sens rom 142 hve
B= Edo, amy
Since = ant = 0,4. (32610 rien as
‘ng that the cones hein equal one another af =O, we
rs = Face een am
Combines wt Eg (125), ti
M os = Mo
a
and (ke) m 433)
The Lub serves a a reminder hat we ate desing with
theca in hich Eis peypendculrt he plane-aincidence
These uo expressions, hic are com
e 10 ofthe Fresnel Equation. Mos ofen one del with
dcksice or vt =
form of tes equations is simply
o: conque, he com
(fie) 15060 meosa 439
A ET
ete denotes the mpd recon cuca
iste tpl envi tie
Cae 2: para tthe plane obinidence in pie
the plane-oFncdence ax shown in Fig 440, Continuity
the tungen components of Fon che side ofthe bound,
Prend # re
ray e before onto ofthe tanger
ie elds
component of
Using he fer ha = ad = ewe an combi
Beas = "eos
NE | case + con =
la) Fear Eco 4)
Wen both mesa forming te nea re dle tht re
e
ENE ==
= ums =
= men en =
One father noten! simplification cun be made using
See's Law, whereupon the revel Fauatons or deere
‘aa come Probe 4.391
sina. a =
rae ea san
Ter er
in cos 9
DETENTE TSF
A nte of auton must ei here. Best in mind
ini, 439 and 4.0 were seecid rater ar. For
nl in Fi. 439 we could ave assed tht E pind
‘eva uberetponB, would have had to be revered wel
od me dame athe ig of 7 wou ave tured out tobe
pose ving the othe amplitud coefficients unchanged.
Thesis apearing in Es (142) through 451 which are
ill dictions selected. The minos sin in Eg, 4.42),
Ein Fie. 4.39. Nonoteles, be aware thatthe ete not
ie Fennel Equations, To avid confusion they matt
4.6.3 Interpretation of the Fresnel Equations
Ets. parce. we se nerd In deteining De
racional amplitads and fu densos a are est and
refute. In addon we stl e concerned with
ate if tht mip be nomad the process
Amplitude Coefficients
overt ere range af @ valve. At nary normal inciden
(9, = 0) he tangents in Eg. (4.43) are sell equ 0
We wil come bck to the physical significance u the minos
mena
mc 8
re = Fone al.
men,
whieh follows as wel from Eas (43) and (30) In Im
sequently
Pres 1er any
‘This equality ofthe election coefficients arses because the
plane of incidence is no longer speciied when 8, = 0. Ths,
neal normal incidence, the amplitude rection coetiients
equal =02, (See Problem 4,5,
Wien, > mi follows fom Snel Law that 0, > Band
+, is negative forall values of O (Fi. 441). In contas Eg,
(4.85) ells ws that rs out postive a = Oand decrees
aradualy until itequals zero when (8 + 8) = AF, since there
‘an 2/2 is infinite. Te particular value of the incident ange
for which this occurs is denoid hy 8, and referred toas the
polarization angle (see Section 86.1) Notice that 7, > Dat
tne E-field do any flipping when 8 approaches 8 from ether
more negative, teaching — LO at 97
this page and Took seat down ino 10, 0
Wen both mesa forming te nea re dle tht re
e
ENE ==
= ums =
= men en =
One father noten! simplification cun be made using
See's Law, whereupon the revel Fauatons or deere
‘aa come Probe 4.391
sina. a =
rae ea san
Ter er
in cos 9
DETENTE TSF
A nte of auton must ei here. Best in mind
ini, 439 and 4.0 were seecid rater ar. For
nl in Fi. 439 we could ave assed tht E pind
‘eva uberetponB, would have had to be revered wel
od me dame athe ig of 7 wou ave tured out tobe
pose ving the othe amplitud coefficients unchanged.
Thesis apearing in Es (142) through 451 which are
ill dictions selected. The minos sin in Eg, 4.42),
Ein Fie. 4.39. Nonoteles, be aware thatthe ete not
ie Fennel Equations, To avid confusion they matt
4.6.3 Interpretation of the Fresnel Equations
Ets. parce. we se nerd In deteining De
racional amplitads and fu densos a are est and
refute. In addon we stl e concerned with
ate if tht mip be nomad the process
Amplitude Coefficients
overt ere range af @ valve. At nary normal inciden
(9, = 0) he tangents in Eg. (4.43) are sell equ 0
We wil come bck to the physical significance u the minos
mena
mc 8
re = Fone al.
men,
whieh follows as wel from Eas (43) and (30) In Im
sequently
Pres 1er any
‘This equality ofthe election coefficients arses because the
plane of incidence is no longer speciied when 8, = 0. Ths,
neal normal incidence, the amplitude rection coetiients
equal =02, (See Problem 4,5,
Wien, > mi follows fom Snel Law that 0, > Band
+, is negative forall values of O (Fi. 441). In contas Eg,
(4.85) ells ws that rs out postive a = Oand decrees
aradualy until itequals zero when (8 + 8) = AF, since there
‘an 2/2 is infinite. Te particular value of the incident ange
for which this occurs is denoid hy 8, and referred toas the
polarization angle (see Section 86.1) Notice that 7, > Dat
tne E-field do any flipping when 8 approaches 8 from ether
more negative, teaching — LO at 97
this page and Took seat down ino 10, 0
ena he glas mil soc decides prayer an he es
iminished appreciably. Now hold ho slide near your eye and
again iow te poe trough yw le creasing The
‘ore ic ee the page trough e glas. When 8
Ste side wl ok ikea pict mio the tection
Se py, saa he Coro ths ok, wl Be mire
se string incidence. Hold he book honizemali th evel
he sure sefieced rater nicely the cover, Things
that ven Xray ald he ior tected glancing ne
As normal incidence Equ (435) and (4:1) led rer
es ma
to the case ol external reflection (i, > a). The oppose
‘tion of feral reflection, ch hc iden med
iss ol eres as vella m
istnce 8, > @ and a described by Eq (42), il
sled hc critical angle, 0. Specialy isthe speci val
eof cent angle p.122) or which 6, = =. Lik
wise, rsa af negatively 16a. (447) a 0, = 0 ant
the Fre Eton (340) Afin ases Mh er
the part al Wise for Problem 2.6 0 sou
reflection athe interface between the same media are simply
eis in Sesion 47, where will be show that rand
Phase Shits
Tsou We vient fom (42 a Re eur
E ing à ob ete opposite Seton. he fis res
iminished appreciably. Now hold ho slide near your eye and
again iow te poe trough yw le creasing The
‘ore ic ee the page trough e glas. When 8
Ste side wl ok ikea pict mio the tection
Se py, saa he Coro ths ok, wl Be mire
se string incidence. Hold he book honizemali th evel
he sure sefieced rater nicely the cover, Things
that ven Xray ald he ior tected glancing ne
As normal incidence Equ (435) and (4:1) led rer
es ma
to the case ol external reflection (i, > a). The oppose
‘tion of feral reflection, ch hc iden med
iss ol eres as vella m
istnce 8, > @ and a described by Eq (42), il
sled hc critical angle, 0. Specialy isthe speci val
eof cent angle p.122) or which 6, = =. Lik
wise, rsa af negatively 16a. (447) a 0, = 0 ant
the Fre Eton (340) Afin ases Mh er
the part al Wise for Problem 2.6 0 sou
reflection athe interface between the same media are simply
eis in Sesion 47, where will be show that rand
Phase Shits
Tsou We vient fom (42 a Re eur
E ing à ob ete opposite Seton. he fis res
aul i
Fig 442 Te ant oia rin a ation
een 1718 .
become a positive quant, The sign of 1, I
decisivo direcion a], and [Es
era af (Es, anemoun: o invodacin a
site with
Aga oracion at the boundary YE, and
i wil be ampara and therefore out-of phase with
‘ch ther as indicate by the negative vale ofr, When we
«ro confision sto whether v0 fields are piano or od
le ¡cof phase. In summary. hen. he component of
tie lec filé normal tthe plan d'incidence undergoes
‘phases of seradians upon reflection when the incident
‘meu has a lower index than the ranvmiting medium.
ara bir lsc obvios won we dal with (EJ.
i now becomes nenn 1 define more explicit
bu gene aot colnet. The field Sections were base in
Figs 439 ar 0 such ati You ook down anyone
the propagation sexism icon rom which he
her my es ce resto
elas im th incident plane are inphase i thei -comps
ent are parallel and are ouf phase J the components
fre antiparallel Nai Bat i eld re oot
‘hs ein we ec nly to a he vet normal o te
planet incidence wher they be Bor Bt etemnir the
Feative phase ofthe accompanying cis he incide
plane. Thus in Fi. Band E, rin his, aro Bard
5. whereasE and Ear coplas donz with Ban
Sharyn Fig ANB, Es. and E arias, as ar
‘Now: the ample elston coccion or the paral
coe nc
whichis postive (Ag) = 0) as longa
sin 060: 0 cos sin > 0
|
gro 443 ct case hits
Fig 442 Te ant oia rin a ation
een 1718 .
become a positive quant, The sign of 1, I
decisivo direcion a], and [Es
era af (Es, anemoun: o invodacin a
site with
Aga oracion at the boundary YE, and
i wil be ampara and therefore out-of phase with
‘ch ther as indicate by the negative vale ofr, When we
«ro confision sto whether v0 fields are piano or od
le ¡cof phase. In summary. hen. he component of
tie lec filé normal tthe plan d'incidence undergoes
‘phases of seradians upon reflection when the incident
‘meu has a lower index than the ranvmiting medium.
ara bir lsc obvios won we dal with (EJ.
i now becomes nenn 1 define more explicit
bu gene aot colnet. The field Sections were base in
Figs 439 ar 0 such ati You ook down anyone
the propagation sexism icon rom which he
her my es ce resto
elas im th incident plane are inphase i thei -comps
ent are parallel and are ouf phase J the components
fre antiparallel Nai Bat i eld re oot
‘hs ein we ec nly to a he vet normal o te
planet incidence wher they be Bor Bt etemnir the
Feative phase ofthe accompanying cis he incide
plane. Thus in Fi. Band E, rin his, aro Bard
5. whereasE and Ear coplas donz with Ban
Sharyn Fig ANB, Es. and E arias, as ar
‘Now: the ample elston coccion or the paral
coe nc
whichis postive (Ag) = 0) as longa
sin 060: 0 cos sin > 0
|
gro 443 ct case hits
Pr 444 se its pe ad ry non
ov uivatenly
Tis willbe he ese form, <mit
arma as
and form, > rte
armen ass
Tios when n,< (EJ nd [Es] il be inphase (Ay =
Drum = 8, and ow ol phase by radians caer, The
transition ist seal discomtin ws, since (E, oes
9%. which means hat Ay, = m. From 9, 100. Is posine
tally tories tow at 8, = 97
Figure 4-0, which sommaries hese conclusions ibe
come wie ow. The art Tusetionl form of Sg emt
Se formal rei nthe veion whos > Osan de
ound in he iterate,” bu th curve pito here wil sul
ice for ou purposes. Figure 4 de ia plo ofthe relive
pave shit between the parle and perpendicear compo
tents tht is Se, Siu is included here beste wi
useful later on cg. when we conier polarization effec
ised in Figs, 445 and 446. The amplitudes of the
rece vexor arc in accord with thon of Figs dan
42 (for an aire) and the phase alfa age
‘ith howe oF Fg LA,
Many of ese canin can De sec with he simples
experiment equipment namely. two car poles,
[ere of gls. md small source. suchas light orig
Smet lamp. By placing one polarizr in Fort ol he sure
(8:45 te plinc-osinidene),youca easily duplicate th
459) o ight wil passthrough the second polarizer is
¿cansion ain spall th planc- incidence. Incom
prison, at nar glancing incidence the eleted beam wi
hen the axes of the uo polarizer a most nora
to cacho
ov uivatenly
Tis willbe he ese form, <mit
arma as
and form, > rte
armen ass
Tios when n,< (EJ nd [Es] il be inphase (Ay =
Drum = 8, and ow ol phase by radians caer, The
transition ist seal discomtin ws, since (E, oes
9%. which means hat Ay, = m. From 9, 100. Is posine
tally tories tow at 8, = 97
Figure 4-0, which sommaries hese conclusions ibe
come wie ow. The art Tusetionl form of Sg emt
Se formal rei nthe veion whos > Osan de
ound in he iterate,” bu th curve pito here wil sul
ice for ou purposes. Figure 4 de ia plo ofthe relive
pave shit between the parle and perpendicear compo
tents tht is Se, Siu is included here beste wi
useful later on cg. when we conier polarization effec
ised in Figs, 445 and 446. The amplitudes of the
rece vexor arc in accord with thon of Figs dan
42 (for an aire) and the phase alfa age
‘ith howe oF Fg LA,
Many of ese canin can De sec with he simples
experiment equipment namely. two car poles,
[ere of gls. md small source. suchas light orig
Smet lamp. By placing one polarizr in Fort ol he sure
(8:45 te plinc-osinidene),youca easily duplicate th
459) o ight wil passthrough the second polarizer is
¿cansion ain spall th planc- incidence. Incom
prison, at nar glancing incidence the eleted beam wi
hen the axes of the uo polarizer a most nora
to cacho
Forthennore the radian ox ens (W/m? or iain e
Te (= SEES I
Ts th verge cay pr ii ria a it aa
normal Si oropi ei Si pare ath
Aa ie AD. an, beth cie rec.
al aras ofthe insider, reflected, nd runsmined Deans ae
respectively. eos, A cos 8, and cos, Acconinsy the
inciden powers A con Otis is he energy per unt ime
For 446
preted Et ais args cnc wih
Reflectance and Transmittance. E
Cac a dicular beam of Wight inciden on a suce, as
hum Fig 7. such that here isan illuminated spt of
24 Real hat the power per nin rosin are
cu whose nal j parallel 18. the Pyatng ver. h
tonty &
= Rx 15:01 Fur 447 Morin ados a mint beam
Te (= SEES I
Ts th verge cay pr ii ria a it aa
normal Si oropi ei Si pare ath
Aa ie AD. an, beth cie rec.
al aras ofthe insider, reflected, nd runsmined Deans ae
respectively. eos, A cos 8, and cos, Acconinsy the
inciden powers A con Otis is he energy per unt ime
For 446
preted Et ais args cnc wih
Reflectance and Transmittance. E
Cac a dicular beam of Wight inciden on a suce, as
hum Fig 7. such that here isan illuminated spt of
24 Real hat the power per nin rosin are
cu whose nal j parallel 18. the Pyatng ver. h
tonty &
= Rx 15:01 Fur 447 Morin ados a mint beam
120. Ener ne ronge Le
and Aco iste power being
ne he eflectance tobe the
power in the refed ba
trated tough 4, We de
fai ofthe elect power fr fbn 10 the incident power
erreichen a and ven
= a
the incide and reed warcs ae in the same medium.
r fo Rel rer ML
eat paca meros, 8 = 6 = 0 inane Fa
rai the appropriate adn We net nt
Sorry about te sin of Fin any pacar formula, and
Eg, (4.57) Y iso simply equal 01. fortwo reasons Fin
pio nergy ranopotd int and ut ol ie:
ice ae deren. in ther won om Ea. 337. Sc
te ae dicen. Te ent low per uit aca alee
er wor ie al ney lowing to ara À per oi ine
TACO = LAC ETAGE (ES
‘When both sides ae maple y thivepresson become
= sn (Bay (nee aN um
OOO
Butthivissimply
R+r=1 a
vere thee was mo born. convenient 10 us 14
{men à “=
= (mesa =
ov Problem 71) at
Peer us
sd métier En
Fae 448 Rt
and Aco iste power being
ne he eflectance tobe the
power in the refed ba
trated tough 4, We de
fai ofthe elect power fr fbn 10 the incident power
erreichen a and ven
= a
the incide and reed warcs ae in the same medium.
r fo Rel rer ML
eat paca meros, 8 = 6 = 0 inane Fa
rai the appropriate adn We net nt
Sorry about te sin of Fin any pacar formula, and
Eg, (4.57) Y iso simply equal 01. fortwo reasons Fin
pio nergy ranopotd int and ut ol ie:
ice ae deren. in ther won om Ea. 337. Sc
te ae dicen. Te ent low per uit aca alee
er wor ie al ney lowing to ara À per oi ine
TACO = LAC ETAGE (ES
‘When both sides ae maple y thivepresson become
= sn (Bay (nee aN um
OOO
Butthivissimply
R+r=1 a
vere thee was mo born. convenient 10 us 14
{men à “=
= (mesa =
ov Problem 71) at
Peer us
sd métier En
Fae 448 Rt
Wien @ = 0. the inciden plane hecome undefined, and
tents of and T vanishes, In hie case Bg. (4.51 through
as
em Taner as
tem, which might have 100 20 such air
Indeed. if u GK pespendicwiay ito as of about
mich inner an
mos ofthe fight wil be
inroacope slider cover glass er ae
aie to handle in large quantities)
feflcted, The stack wil lok very much ike mio (se
photo) Rolls an shat of lear plo to mre
{inde and to wil ok ke him tal The many ten
aces produce = lege numberof closely peed ro
reflections tht end much of te Hig back the insert
medium, more oes, al undergone «ingle rie
independent reflection. A smooth ray metal tac Sos
ety much he same hing
pendent specular titane nd looks
Shiny) Wake flection ic, the ware wil appar
ray oresen white le relance e largo enough
ar. Figure 450 dpi th corresponding dependence of the
France at ama inidence on e mero: erases
ande index ofthe medium, OF
sec tough roll of "car stoat-suaced lav ae, and
¡es ale the many elements ina penscope mos he costed
isthe why ou cat
‘sags Hae Espace Ka ai ki oad
tents of and T vanishes, In hie case Bg. (4.51 through
as
em Taner as
tem, which might have 100 20 such air
Indeed. if u GK pespendicwiay ito as of about
mich inner an
mos ofthe fight wil be
inroacope slider cover glass er ae
aie to handle in large quantities)
feflcted, The stack wil lok very much ike mio (se
photo) Rolls an shat of lear plo to mre
{inde and to wil ok ke him tal The many ten
aces produce = lege numberof closely peed ro
reflections tht end much of te Hig back the insert
medium, more oes, al undergone «ingle rie
independent reflection. A smooth ray metal tac Sos
ety much he same hing
pendent specular titane nd looks
Shiny) Wake flection ic, the ware wil appar
ray oresen white le relance e largo enough
ar. Figure 450 dpi th corresponding dependence of the
France at ama inidence on e mero: erases
ande index ofthe medium, OF
sec tough roll of "car stoat-suaced lav ae, and
¡es ale the many elements ina penscope mos he costed
isthe why ou cat
‘sags Hae Espace Ka ai ki oad
Fieve 450 Tran
4.7 Total Internal Reflection
titel ame. Las mu at sation race
Sie awe on he pin in Pie
ver 8 > since
sin = "ung,
co > which ese Ti O PCO Trg
the Suns ay gradual, approaches tangeny with he
day and at dont ore ad more ae ovale eer
Y appears inthe reitet beam. Final, when 6, = 90
spa u
As noed cali, he critical angle is tha special al of @
fr hich @ = 9°. Th age mi these ys and te
smaller ls. ocinciden anges rater than or egal 08.
the incoring energy elle bask ino the inciden me
taint pres brow a ttl infernal reflec om =p
ho be res ht e nso rom he sonne
any dscontimies, As 8 Decames larger, e elected bean
[rows sronger and sronzer wile the teamed Beam prom
Wecker, unl the later vanishes and the former cie af a
the energy u 0, = 8. I's an easy mater 10 observe the
“diminuto of he transmite Beam as @ x mad larger Ju
place a lace microscope slide on sprinted pe, this ime
Docking out any spocuany reflected light. At 9 0, 9
bright and clear. But you move your head, allowing @ he
Nos
4.7 Total Internal Reflection
titel ame. Las mu at sation race
Sie awe on he pin in Pie
ver 8 > since
sin = "ung,
co > which ese Ti O PCO Trg
the Suns ay gradual, approaches tangeny with he
day and at dont ore ad more ae ovale eer
Y appears inthe reitet beam. Final, when 6, = 90
spa u
As noed cali, he critical angle is tha special al of @
fr hich @ = 9°. Th age mi these ys and te
smaller ls. ocinciden anges rater than or egal 08.
the incoring energy elle bask ino the inciden me
taint pres brow a ttl infernal reflec om =p
ho be res ht e nso rom he sonne
any dscontimies, As 8 Decames larger, e elected bean
[rows sronger and sronzer wile the teamed Beam prom
Wecker, unl the later vanishes and the former cie af a
the energy u 0, = 8. I's an easy mater 10 observe the
“diminuto of he transmite Beam as @ x mad larger Ju
place a lace microscope slide on sprinted pe, this ime
Docking out any spocuany reflected light. At 9 0, 9
bright and clear. But you move your head, allowing @ he
Nos
eprint page covered by elas wi appear darker and
"Te crcl angle frou arpas trace roughly 42
TABLE 42 Criical Angles
fe of either of the priv in Fig. 452 wll have 00,
and therefore be ltermally reflected Ti is convenient
ay reflet mery 100% ofthe incident ight witout ha
ingto wer about he detention that can occur ih et
races ce photo),
[Another fat way to veu the situation via Fi
Atomic oss tre We Eno hate net fc e presence
‘ofthe homogeneous ori media falter the peed ofthe
Tight ram cto nd o, respectively 49-92): The tesla
ae the superposition ofthese waves propa a he
the mission of wavelets sucesivel fom salten centers
selected wave, which comes back down into the incident
den ro wave a distance = CB, while the ramited
front moves a distance of = AD > CB. Since one wave
"Te crcl angle frou arpas trace roughly 42
TABLE 42 Criical Angles
fe of either of the priv in Fig. 452 wll have 00,
and therefore be ltermally reflected Ti is convenient
ay reflet mery 100% ofthe incident ight witout ha
ingto wer about he detention that can occur ih et
races ce photo),
[Another fat way to veu the situation via Fi
Atomic oss tre We Eno hate net fc e presence
‘ofthe homogeneous ori media falter the peed ofthe
Tight ram cto nd o, respectively 49-92): The tesla
ae the superposition ofthese waves propa a he
the mission of wavelets sucesivel fom salten centers
selected wave, which comes back down into the incident
den ro wave a distance = CB, while the ramited
front moves a distance of = AD > CB. Since one wave
{C0 a since they have the same frequency aná peros,
they mst change phate be the sare apo ih process.
“This ie distrae ul pnt F mus he in-phase with hat ot —
font remember Seton
can be seen ha ie great sin comparison 0 e
be. That much is depicted in Fig, 4.530, where ls Bsn
her speed, teasing AD and causing a greater wane
TETE PE 53e Spe ETES A0
AB = 77, and wavelets wi vera in-phase ef aa
Pete M From ple ABC: 0
refer = mm. which iq 04:69) For the wo piven meda
Ge. for he pail valve of he direcion in which
‘carered wavelets wi dd onsrictvely i the transit
medium along ie interface. The esling disturbs (B=
07 ie known at surface wu
4.7.1 The Evanescent Wave
Because th query of X-rays higher han te resonar
and experiments confi, thatthe index of reaction of X
inthe Gent se When rayo unchng tren
denne trl ke gas. the beam bends avr a SIEM
<u oh ora ae han ward Wh de eve
sn inet seen mind ve all
0 expen has Xap wil De aly “externally” eis
fo gaan oe meses nv Pe ee it often spoken of inthe erature, but that's a misnomer
Enr on le ya ore ene an a, he pros
y
they mst change phate be the sare apo ih process.
“This ie distrae ul pnt F mus he in-phase with hat ot —
font remember Seton
can be seen ha ie great sin comparison 0 e
be. That much is depicted in Fig, 4.530, where ls Bsn
her speed, teasing AD and causing a greater wane
TETE PE 53e Spe ETES A0
AB = 77, and wavelets wi vera in-phase ef aa
Pete M From ple ABC: 0
refer = mm. which iq 04:69) For the wo piven meda
Ge. for he pail valve of he direcion in which
‘carered wavelets wi dd onsrictvely i the transit
medium along ie interface. The esling disturbs (B=
07 ie known at surface wu
4.7.1 The Evanescent Wave
Because th query of X-rays higher han te resonar
and experiments confi, thatthe index of reaction of X
inthe Gent se When rayo unchng tren
denne trl ke gas. the beam bends avr a SIEM
<u oh ora ae han ward Wh de eve
sn inet seen mind ve all
0 expen has Xap wil De aly “externally” eis
fo gaan oe meses nv Pe ee it often spoken of inthe erature, but that's a misnomer
Enr on le ya ore ene an a, he pros
y
‘an bu very nearly elo, the nde ul = Vand 8
tn 1925 A. Compton reasoned that ven though X-rays
lcd, ey shouldbe totally “enteall” elect at
aneing incidence He shin 0.12 nm X-rays on a glas
alte and got crieal angle of about 10 minutes of ac
(U167) measured wih respect he ue. That cdd an
1 oth tot internal ad vl “eterna lc ar on
If we assume in the cave of total internal reilection that
he boundary conditions wing ny he inciden and refed
waves dins ate noc a alla imple as they might sem,
Fermer, can eformlate Ego 4) (440) (rob
so & = in = si 8)
am
O
CUS
come complex quant. Despie th Problem 4.767,
rte Land R= Y which means Mat, = and 6
Ihe aueh er ma amande cam,
peor te complte and ae leg, computation needed
do deiv expressions forall the reflected and tite
clé, but we cn pet an appreciation of har’ happen an
‘te following way Te wavefucton forthe tated le
Fs ep w
a seen in Fig. 454, Once agan wine Sal La
wn
} 67m
Ben a= zufı
or since we are consemed with he ese ero sin > 1
Nenleting the positive exponent, which is physically
antenne ne ha a wae whose ampitade rope a exo
tance advances in ne x-direction a surface or evanescent
ave Notice atthe wavelons or surface of constant pase
{parle they plane) ae perpendicular the ares 0
wave infomosencoas p26) Re amplitud decays ply
Fate y direcion, becoming nee ata distance ie he
I yanare sil concerned about he conservation of ery.
more extensive es would have shown tat ner
Gal sles ask and fort sors he merce sal
the second medium. Yet one puzzling point remains, ras
Figo 45 Proa victor o ena etn
tn 1925 A. Compton reasoned that ven though X-rays
lcd, ey shouldbe totally “enteall” elect at
aneing incidence He shin 0.12 nm X-rays on a glas
alte and got crieal angle of about 10 minutes of ac
(U167) measured wih respect he ue. That cdd an
1 oth tot internal ad vl “eterna lc ar on
If we assume in the cave of total internal reilection that
he boundary conditions wing ny he inciden and refed
waves dins ate noc a alla imple as they might sem,
Fermer, can eformlate Ego 4) (440) (rob
so & = in = si 8)
am
O
CUS
come complex quant. Despie th Problem 4.767,
rte Land R= Y which means Mat, = and 6
Ihe aueh er ma amande cam,
peor te complte and ae leg, computation needed
do deiv expressions forall the reflected and tite
clé, but we cn pet an appreciation of har’ happen an
‘te following way Te wavefucton forthe tated le
Fs ep w
a seen in Fig. 454, Once agan wine Sal La
wn
} 67m
Ben a= zufı
or since we are consemed with he ese ero sin > 1
Nenleting the positive exponent, which is physically
antenne ne ha a wae whose ampitade rope a exo
tance advances in ne x-direction a surface or evanescent
ave Notice atthe wavelons or surface of constant pase
{parle they plane) ae perpendicular the ares 0
wave infomosencoas p26) Re amplitud decays ply
Fate y direcion, becoming nee ata distance ie he
I yanare sil concerned about he conservation of ery.
more extensive es would have shown tat ner
Gal sles ask and fort sors he merce sal
the second medium. Yet one puzzling point remains, ras
Figo 45 Proa victor o ena etn
be odo; nc plans of incidence. Since ths mery
‘ld or hve penetrated mote ls done medias under
fone would obvios te roma ue plane wave. This devi
octal cs clea fom chend dmg. 44 habe
in phase by nd cannot eros ance each tb If
Ho fot contin of ie tangent component of E
i there mt De an oct il ne ee deme med
[dens fete anse une)
pressed nother piece llas ain the ith ta
nero ould be made to vanish, and he Beem would then
propaga onward unditubed. Funhermee, you mie
figuras. dtchy pecmiting enengy 1 How. Figure 4.35
‘eet scent sopreenation of FER he width of he
inca doting the wavefronts decrease crete
Fe as rast
hat he apd of ei Rem he sam
remarque
‘One ca demon FTIR wih he pu amangomen of
il ihe can be posiioned so ast ram and eect any
index transparent ila precision sper, Low dons elo
Cong TO UG ate a woul a ca QUE
‘Onc can duplicate the above apical espemen with old
ere DCE LA ane of these OU BE
mars 1 cir te dependence ofthe Held amie 0
‘ld or hve penetrated mote ls done medias under
fone would obvios te roma ue plane wave. This devi
octal cs clea fom chend dmg. 44 habe
in phase by nd cannot eros ance each tb If
Ho fot contin of ie tangent component of E
i there mt De an oct il ne ee deme med
[dens fete anse une)
pressed nother piece llas ain the ith ta
nero ould be made to vanish, and he Beem would then
propaga onward unditubed. Funhermee, you mie
figuras. dtchy pecmiting enengy 1 How. Figure 4.35
‘eet scent sopreenation of FER he width of he
inca doting the wavefronts decrease crete
Fe as rast
hat he apd of ei Rem he sam
remarque
‘One ca demon FTIR wih he pu amangomen of
il ihe can be posiioned so ast ram and eect any
index transparent ila precision sper, Low dons elo
Cong TO UG ate a woul a ca QUE
‘Onc can duplicate the above apical espemen with old
ere DCE LA ane of these OU BE
mars 1 cir te dependence ofthe Held amie 0
4.8 Optical Properties of Metals
128 Chapter a Ts Ppt a
À monzre und line In ont, an deve "perfect" con
actor would have a indie contre This galet
tm saying tha the clectons driven i scilsin by a hr
There woul be no resina ose no natal fequecies and
cco aig colision with bernal aged ic
ox wil parlons and in so doing reverb convert
Closnanaymc nergy in ole es. Te api of ra
nt energy y à material à function of es onductvi
Waves in a Metal
lí ue aie he medium a continuous, Maxwells que
uo ait, isa Borde time derivative, like the damping
(Of FE genera a vole, current iento, and ico the
ng absapion. Ti expresion can De educ othe ut
compe quam Ts in tum lead 0a complex Index of
veto ct, as We sa eae p71) AMON
Aaron, We ten need only sant the complex inden
‘ere he ead asian ne ad a bol eal
ster) note comesponding olmos fora encore
medium Ahemal cl. we cu lieth wane equation and
either even, tis possible 0 find a Simple snusoidat plane
pra he rein is ordinal wen as
a een TER IE WA
precisa y were the mor usual index of erin: A
De Wave progres io me conduc, amplitude, Ey exp
une à exponemialy sievenel,Lnsnuch tira
‘nce portional ot square lt umplnde, we
where f= HD) ati, fs te ivan sy = Oh ine
face), anda cis called the absorp
{even beter) the attenuation coefficient, The lux dens
will drop hy à factor of e. "= 1/27 after the wave hs
propagated a distance» = 1/a,kaownas he skin or penetra.
on depth For a material tobe transparent. the penet
epi rust be large in comparison ots hiess. The pee
tration dpe or metals. however is excecdinly small. Fa
suple. copper a uluavioet wavelengths = 100 nm) his
only about 6 nm in the infrared (Ae = 10000 nm). Tis
nonetheless can become pry tasparent when formed int
‘way minors), he falar metallic sheen of conductors core
Sponds o à high reNecian, which exists because the incide
wave cannot effectively penetats tb meteria. Relatively few
Tore. though each ssonbs strongly. ile etal energy i dis
sipaled by them. stead. most of the incoming ener
reappears as the reflected wave, The majority of meta
including the less common ones (8, sodium, potassium.
«cesium. vanadium. piobium. gadliniun. holmium.yurium
‘scandium, and os) have asilvery gay appearance like
dent igh roughly 851009) regards of wavelengths and
are therefore eset iones
[Equation (1277) is certainly reminiscent of Eq (4.73) and
ude. Moreover, a complete analysis would show thatthe
on of pavagaton a both
À monzre und line In ont, an deve "perfect" con
actor would have a indie contre This galet
tm saying tha the clectons driven i scilsin by a hr
There woul be no resina ose no natal fequecies and
cco aig colision with bernal aged ic
ox wil parlons and in so doing reverb convert
Closnanaymc nergy in ole es. Te api of ra
nt energy y à material à function of es onductvi
Waves in a Metal
lí ue aie he medium a continuous, Maxwells que
uo ait, isa Borde time derivative, like the damping
(Of FE genera a vole, current iento, and ico the
ng absapion. Ti expresion can De educ othe ut
compe quam Ts in tum lead 0a complex Index of
veto ct, as We sa eae p71) AMON
Aaron, We ten need only sant the complex inden
‘ere he ead asian ne ad a bol eal
ster) note comesponding olmos fora encore
medium Ahemal cl. we cu lieth wane equation and
either even, tis possible 0 find a Simple snusoidat plane
pra he rein is ordinal wen as
a een TER IE WA
precisa y were the mor usual index of erin: A
De Wave progres io me conduc, amplitude, Ey exp
une à exponemialy sievenel,Lnsnuch tira
‘nce portional ot square lt umplnde, we
where f= HD) ati, fs te ivan sy = Oh ine
face), anda cis called the absorp
{even beter) the attenuation coefficient, The lux dens
will drop hy à factor of e. "= 1/27 after the wave hs
propagated a distance» = 1/a,kaownas he skin or penetra.
on depth For a material tobe transparent. the penet
epi rust be large in comparison ots hiess. The pee
tration dpe or metals. however is excecdinly small. Fa
suple. copper a uluavioet wavelengths = 100 nm) his
only about 6 nm in the infrared (Ae = 10000 nm). Tis
nonetheless can become pry tasparent when formed int
‘way minors), he falar metallic sheen of conductors core
Sponds o à high reNecian, which exists because the incide
wave cannot effectively penetats tb meteria. Relatively few
Tore. though each ssonbs strongly. ile etal energy i dis
sipaled by them. stead. most of the incoming ener
reappears as the reflected wave, The majority of meta
including the less common ones (8, sodium, potassium.
«cesium. vanadium. piobium. gadliniun. holmium.yurium
‘scandium, and os) have asilvery gay appearance like
dent igh roughly 851009) regards of wavelengths and
are therefore eset iones
[Equation (1277) is certainly reminiscent of Eq (4.73) and
ude. Moreover, a complete analysis would show thatthe
on of pavagaton a both
The serein of meal continuous medium works
sy well nthe low-frequensy long wareengi doma of
de infrared Yet ue cetlls mi expt tha as he wave
Tenth of the incident Beam decrease the atta anal
cortina mode shows lage dscrepancies fom exprime
Lanz, Paul Kal Ldn Drud (1863-1906), an thers
Time appesch wll provide qualite agreement with
The Dispersion Equation
Envision the conductor a an assemblage of driven, duped
valine: Some conespone to re lesions an wil there
have eo restoring Ins, wheres es re Bd oh
xe, much ike hove nthe delet medi of Seton 3.1
The conduction electrons ae, however, the predomina com
‘sorta the opal proper of metas, Real Has the di
71 1661
in sent te driving force q, E) and therefore 180° out-of
pase with i, This is unlike the situation for transparent
tickets, where the resonance Irequencies ae above he vs:
ite andthe electrons exile in-phase withthe diving force
(Fig, 457), Free elections oscillting out-of-phase with the
‘ecient light will eadiate wavelets that tend to cancel the
incoming disturbance. The effect, as we have aredy seen e
arid decaying refracted wave
‘avin about within a conductors just the applied filé E.
G72 coread
ts herein Vis the umber of atom pr anit ome ch
"48 oot Proper rm 128
ideal o (3.72) should he nord that a meza as
à particular olor, indices at the stm ate partie
Seles bp by way ofthe bod lesen aldo
tothe genera ahsorlion she Ge re ees
Recal hat mer tht very stony sob at i=
en roquney does actully absorb ms ofthe nid
and copper are dis yellow bas y res mi nate
Feng andthe age ales of ae elected mor tong.
Ths fo example, gold shuld aly page to te ont
Fos ese than roughly 10" m thick wil nd ran pre
ty making 4 few simplifying wsumptions. Acconlney
elect the hound ler cotation an sue that,
sy well nthe low-frequensy long wareengi doma of
de infrared Yet ue cetlls mi expt tha as he wave
Tenth of the incident Beam decrease the atta anal
cortina mode shows lage dscrepancies fom exprime
Lanz, Paul Kal Ldn Drud (1863-1906), an thers
Time appesch wll provide qualite agreement with
The Dispersion Equation
Envision the conductor a an assemblage of driven, duped
valine: Some conespone to re lesions an wil there
have eo restoring Ins, wheres es re Bd oh
xe, much ike hove nthe delet medi of Seton 3.1
The conduction electrons ae, however, the predomina com
‘sorta the opal proper of metas, Real Has the di
71 1661
in sent te driving force q, E) and therefore 180° out-of
pase with i, This is unlike the situation for transparent
tickets, where the resonance Irequencies ae above he vs:
ite andthe electrons exile in-phase withthe diving force
(Fig, 457), Free elections oscillting out-of-phase with the
‘ecient light will eadiate wavelets that tend to cancel the
incoming disturbance. The effect, as we have aredy seen e
arid decaying refracted wave
‘avin about within a conductors just the applied filé E.
G72 coread
ts herein Vis the umber of atom pr anit ome ch
"48 oot Proper rm 128
ideal o (3.72) should he nord that a meza as
à particular olor, indices at the stm ate partie
Seles bp by way ofthe bod lesen aldo
tothe genera ahsorlion she Ge re ees
Recal hat mer tht very stony sob at i=
en roquney does actully absorb ms ofthe nid
and copper are dis yellow bas y res mi nate
Feng andthe age ales of ae elected mor tong.
Ths fo example, gold shuld aly page to te ont
Fos ese than roughly 10" m thick wil nd ran pre
ty making 4 few simplifying wsumptions. Acconlney
elect the hound ler cotation an sue that,
120 Onaser Te Feat! Uae
als negligible for very anew. whereupon
The later assumption based onthe fact ara ih requ
cies the electrons will undergo a great many oscillations
inametal maybe thowghtof aa plasma whose density ox
Fes a tura frequency ui plasma frequency. Thin.
tum canbe shown to qual eum), ndo
The plasma frequency serves as a erica value below which
the index is complex andthe penetrating wave drops off
above, mi eal absorption is small, andthe conductors
as for lletres u very high requencies tocan be greater
be fairly transparent o X-rays. Table 4.3 lists the plain fe
‘quencies for some ofthe kai metal that ae transparent
The index of rercion or a meta wil sy be comple,
and ie impinging wave will ufer absorption fn an amount
tate Frequency dependent. For example. he outer von un
"he Apolo space sus were one with a sty din Km 0
die photo). The coming reflet about 70% ofthe nc
‘eight and was sed under Drigh condition, auch as low
aa forward Sus angles It was designed decrease the er
‘al nd on the cooling sytem by strongly retin radiant
erg incre wie sil ani adequately the
TABLE A Critical Wavolongthe and
Frequencies for Some Alkal Metals
(observed) (calculated) cobscrved)
Met am m ir
‘Similar in principle are slo avilable commercial. and
they're wel wont having ost o Experiment wi
"The lonied upper atmosphere ofthe Earth consis ade
ibn o re elctons that Behave very mach like those
‘ci wi be real and es an fo quences above,
In July of 1965 the Mariner IV spacecraft made use of bs
eco examine the ionosphere ofthe planet Mas, 216 mi
Ton lometers rom Earth
Ir we wish 6 communicate between two distant eesti
pains, we might bounce low frequency waves of the Fans
Ionosphere To speak to someone onthe Moon however, we
Should oe high frequency sina, o which he tonosphere
Reflection from a Metal
Imagine ba pane wave initial in ai mpinges on a con
ducting surface, The transmited wave advarcing at some
{uctivity of the medium is increased. the wavefrons will
became aligged withthe surface of constant amplitude
thereupon an G, wil approach parallelism. I oer
als negligible for very anew. whereupon
The later assumption based onthe fact ara ih requ
cies the electrons will undergo a great many oscillations
inametal maybe thowghtof aa plasma whose density ox
Fes a tura frequency ui plasma frequency. Thin.
tum canbe shown to qual eum), ndo
The plasma frequency serves as a erica value below which
the index is complex andthe penetrating wave drops off
above, mi eal absorption is small, andthe conductors
as for lletres u very high requencies tocan be greater
be fairly transparent o X-rays. Table 4.3 lists the plain fe
‘quencies for some ofthe kai metal that ae transparent
The index of rercion or a meta wil sy be comple,
and ie impinging wave will ufer absorption fn an amount
tate Frequency dependent. For example. he outer von un
"he Apolo space sus were one with a sty din Km 0
die photo). The coming reflet about 70% ofthe nc
‘eight and was sed under Drigh condition, auch as low
aa forward Sus angles It was designed decrease the er
‘al nd on the cooling sytem by strongly retin radiant
erg incre wie sil ani adequately the
TABLE A Critical Wavolongthe and
Frequencies for Some Alkal Metals
(observed) (calculated) cobscrved)
Met am m ir
‘Similar in principle are slo avilable commercial. and
they're wel wont having ost o Experiment wi
"The lonied upper atmosphere ofthe Earth consis ade
ibn o re elctons that Behave very mach like those
‘ci wi be real and es an fo quences above,
In July of 1965 the Mariner IV spacecraft made use of bs
eco examine the ionosphere ofthe planet Mas, 216 mi
Ton lometers rom Earth
Ir we wish 6 communicate between two distant eesti
pains, we might bounce low frequency waves of the Fans
Ionosphere To speak to someone onthe Moon however, we
Should oe high frequency sina, o which he tonosphere
Reflection from a Metal
Imagine ba pane wave initial in ai mpinges on a con
ducting surface, The transmited wave advarcing at some
{uctivity of the medium is increased. the wavefrons will
became aligged withthe surface of constant amplitude
thereupon an G, wil approach parallelism. I oer
R= forthe sm
Let's now compute the electro
EY an
«seal diet, whereupon in principle the inde is real m
‘andthe atenaton seele. ie. Under those
and e reecance E, ( D) becomes ential wth at of
ER. (67. sad m, I lang wile mei comparsively
Amal, in ta becomes lange (Problem 481). I he una
inal iit were A pure imaginar 100% of the int
‘kare dei would he rest = D. Noe ta its
prs forthe eletnce o one metal reir han at
89.3 nm the parameters associated with slid sodium are
ra me = 00,04 = 24, and = 09: and Boe fr bulk
single ental ng = 37.1 = 5.088 = 07.
‘The curves of R, and, for oblique incidence shown in
109 forte in we ight ih wo metas ve elestinces
Fae ass Des
‘Wat are quie Siri shape: approaching 100 = 90
astas with lle (Fig. 4.0. op à minimum at
reflectance at normal incidence for a numberof evaporated
metal ims unde eal conditions Observe tata god
transit fay welinand below te prec lon of tee:
trun vr, whichis highly elective across the vse
y seccion off a mea ocur in
tothe planeo incidence). These ar ercral eter One
witha notable exception at» whee, usas wih 3
4.9 Familiar Aspects of the Inter-
action of Light and Matter
‘St we saw eal 4p. 77), ight that contains copy
Spectr perceived we. À Broad some ow ight
eier natural or aii eon oe which vey pin on
A ace cn be imagined as ening out za fig
very vse que Given hit us eve on hie par,
Let's now compute the electro
EY an
«seal diet, whereupon in principle the inde is real m
‘andthe atenaton seele. ie. Under those
and e reecance E, ( D) becomes ential wth at of
ER. (67. sad m, I lang wile mei comparsively
Amal, in ta becomes lange (Problem 481). I he una
inal iit were A pure imaginar 100% of the int
‘kare dei would he rest = D. Noe ta its
prs forthe eletnce o one metal reir han at
89.3 nm the parameters associated with slid sodium are
ra me = 00,04 = 24, and = 09: and Boe fr bulk
single ental ng = 37.1 = 5.088 = 07.
‘The curves of R, and, for oblique incidence shown in
109 forte in we ight ih wo metas ve elestinces
Fae ass Des
‘Wat are quie Siri shape: approaching 100 = 90
astas with lle (Fig. 4.0. op à minimum at
reflectance at normal incidence for a numberof evaporated
metal ims unde eal conditions Observe tata god
transit fay welinand below te prec lon of tee:
trun vr, whichis highly elective across the vse
y seccion off a mea ocur in
tothe planeo incidence). These ar ercral eter One
witha notable exception at» whee, usas wih 3
4.9 Familiar Aspects of the Inter-
action of Light and Matter
‘St we saw eal 4p. 77), ight that contains copy
Spectr perceived we. À Broad some ow ight
eier natural or aii eon oe which vey pin on
A ace cn be imagined as ening out za fig
very vse que Given hit us eve on hie par,
122 hap & The Poss
rum resembles that the Su, Simi, a een
appear whi highly rl, fequeny independent. di
july catering bjt wil be preted white under white
Although wate i esca tampa
appears white as des ground lass. The macon 1 simple
‘rough Re pal sie eal but large than he wave
feng mola, ight wil enter each tramparer patie,
‘eft and rc, and merge Tse wil ben dst
Gon among ay othe Feeney components othe el
mechan acco th whiteness ing sa
‘ox gra or ie of wich acy em
Silay. a Madden pise of crumpled clear pla
soap wl appear whitish, a wil an rm art
Iterated witha ar bbls, saving crest or
tater eg wie). ven gh we sal chk of ape a
Spe wit satis, Us an easy mar ode is
Smespion Covers psa pape wha lew fe na
Amina rom bein. You'll Nave ite dil en
tough hm. Int ae ie ato sly pinte
iu, res, an ely trampas eli or example
are nde fran, cr wl nc cle
tn a ean Boundaries. The parc wl ingly dap
Sect ith ines are markedly deen, there wll ea
od ei reflection tal wens Problem 72a
the pin wil apcar white and opaque la anaber ook 3
Ba LEO, Trent pain om cut ony ye he parks so
thay sob al queno eco the dered unge
inthe revere direction, we rede
the pain or fiber boundaries. the
Carrying the 1
tiles of aerial wil eet ev, thereby decreasing the
Overall whence ofthe object, Conreguenly a wet white
tissue wil ive a grayish, more transparent lock, Wet even
lnc it parking whiteness, becoming dl ra
vie soaked ia leur liquid rg. water un, or benzene) wil)
Jose its whitish haze and become much durer. the colons
then bing desp and rich hike howe o alle watersolor
Zi
A difsely esting sora a bo some tn
form aro the spt wl eet bit lve thin a te
rum resembles that the Su, Simi, a een
appear whi highly rl, fequeny independent. di
july catering bjt wil be preted white under white
Although wate i esca tampa
appears white as des ground lass. The macon 1 simple
‘rough Re pal sie eal but large than he wave
feng mola, ight wil enter each tramparer patie,
‘eft and rc, and merge Tse wil ben dst
Gon among ay othe Feeney components othe el
mechan acco th whiteness ing sa
‘ox gra or ie of wich acy em
Silay. a Madden pise of crumpled clear pla
soap wl appear whitish, a wil an rm art
Iterated witha ar bbls, saving crest or
tater eg wie). ven gh we sal chk of ape a
Spe wit satis, Us an easy mar ode is
Smespion Covers psa pape wha lew fe na
Amina rom bein. You'll Nave ite dil en
tough hm. Int ae ie ato sly pinte
iu, res, an ely trampas eli or example
are nde fran, cr wl nc cle
tn a ean Boundaries. The parc wl ingly dap
Sect ith ines are markedly deen, there wll ea
od ei reflection tal wens Problem 72a
the pin wil apcar white and opaque la anaber ook 3
Ba LEO, Trent pain om cut ony ye he parks so
thay sob al queno eco the dered unge
inthe revere direction, we rede
the pain or fiber boundaries. the
Carrying the 1
tiles of aerial wil eet ev, thereby decreasing the
Overall whence ofthe object, Conreguenly a wet white
tissue wil ive a grayish, more transparent lock, Wet even
lnc it parking whiteness, becoming dl ra
vie soaked ia leur liquid rg. water un, or benzene) wil)
Jose its whitish haze and become much durer. the colons
then bing desp and rich hike howe o alle watersolor
Zi
A difsely esting sora a bo some tn
form aro the spt wl eet bit lve thin a te
‘hg, absorb almost all ae igh rd appears bck,
race hal elects perl 70% or DS or mar, bt dos
cal, wil appear te familia shiny gy of 2 pc
quere y ae ot Bound oe som ar ans acia
ander of magnitude larger than they wer or he bound
eos The cien ight cannot pe hema
sy ase aa action a atenga etre sca
the energy is elected ot, and aly the mal remaider 1
dared: Now ta the primary difference been a ra a
sein Anas pins pic oF polishe white met
much a silver or aim hy esting” images o
Ding he room nop pray arre
‘Wher edition of energy in hear of ight ot
eich lor acre th pect the igh apes co
‘Sa ald be peceved as fed pee, and ble light These
bes great dal of variation in the tbo. aná ty wil
roma the responses of re ge, nd le. ne ely
«ould be generated by mixing three hears of gt. provided
‘err frequencies were widely separe When see sch
Sams comi in predoce wie ei they ar al
tor do they have to be quasimonochromatic. Since a wide
nde YB) thee tnd 1 e sed mos oque. They a
dre component (emite by thee phosphors) at pene
fis woe gato Hos sen on colo tlvison sh
‘Any coord ight ham sh ogee aie hi
‘aid tobe complementary un nt ae rn
R-u+G-w
R-u =W-GeM
M-¥=R+h-R+G=WER
The rst robin ok Tt
background ol hie “
ser the sy to pp Be Pang ater ic
the wen Th increases wand he ulaviok They ec
race hal elects perl 70% or DS or mar, bt dos
cal, wil appear te familia shiny gy of 2 pc
quere y ae ot Bound oe som ar ans acia
ander of magnitude larger than they wer or he bound
eos The cien ight cannot pe hema
sy ase aa action a atenga etre sca
the energy is elected ot, and aly the mal remaider 1
dared: Now ta the primary difference been a ra a
sein Anas pins pic oF polishe white met
much a silver or aim hy esting” images o
Ding he room nop pray arre
‘Wher edition of energy in hear of ight ot
eich lor acre th pect the igh apes co
‘Sa ald be peceved as fed pee, and ble light These
bes great dal of variation in the tbo. aná ty wil
roma the responses of re ge, nd le. ne ely
«ould be generated by mixing three hears of gt. provided
‘err frequencies were widely separe When see sch
Sams comi in predoce wie ei they ar al
tor do they have to be quasimonochromatic. Since a wide
nde YB) thee tnd 1 e sed mos oque. They a
dre component (emite by thee phosphors) at pene
fis woe gato Hos sen on colo tlvison sh
‘Any coord ight ham sh ogee aie hi
‘aid tobe complementary un nt ae rn
R-u+G-w
R-u =W-GeM
M-¥=R+h-R+G=WER
The rst robin ok Tt
background ol hie “
ser the sy to pp Be Pang ater ic
the wen Th increases wand he ulaviok They ec
134 Gage 4 Th Peso Li
|
Fier 42 Special eine wre Dae
he selectivo section ur scan ol yellow sed ight that
tke loe he suce la gold il nd e concomitant
Fate o lc gon igh
The character ol mos ubstances ave ther or
nin he phenomenon of sélective or preferential absorp
Son. For example. water his a very faint grcen-bne Ua
cas it sorption of red Hight That the HO moe
lo Nea rbd Fes in te are, which extends
stot no the sb The sorption ST vey song, o
tues a aceetunednflection of red igh a the surtace
toscas ranted and gradually absorbed Ut
deo
boat 30 m of scale, reds almost completely
oa te sul This Same proces of selective
shorron's espns or the colors af row eye and hut
Actes of bits and bes and cabges and kings Inde e
lary of objet in nature appear o have character
ol se result of preferential absorption by pement
eos n contas with most atom: and moles, which
Jan romane in the ultraviolet and fared, Ue pigment
sible pers have energie af roughly 1.6 eV 10 3.2 eV
hi yu might expect, ae on he low se for ordinary
{lest and on te high side or excitan via mo
cum m. Despite thi these
and tons he configuration ofthese sells provide
mad oo cry entation. addition. there he go
To franc dye molecules, which evideily aso have
resonances inthe visible, Al such substances, wheter nu
y conjgate system Tie acta typified by the caso
molecule Case Fi. 4.63). The erolenoids range in colt
from yellow Io re and are found in carol, tomatoes, ds
pls ar amater group of tir atra prets, batho
A ponion ofthe lng chain is tured round on el to forme
fing ln any event, conjugated system ofthis sor contain à
numberof patulry mobil letons known a pi electrons,
They are not bound o spécifie atome sites but insend cu
range over the relavely large dimensions ofthe molecu
‘hai or sng nthe prascology of Quantum Meche
ay tha these ae long-wavelength low-frequency and here
fore low-energy. elsron sates he encre required tore
à pi electron to am exited wate is comparatively low, ome
pong to ha oF visible photons. In efet te molecule cin
Imagine a an Or having «resonance HUE I
the vis,
CRT mc.
|
Fier 42 Special eine wre Dae
he selectivo section ur scan ol yellow sed ight that
tke loe he suce la gold il nd e concomitant
Fate o lc gon igh
The character ol mos ubstances ave ther or
nin he phenomenon of sélective or preferential absorp
Son. For example. water his a very faint grcen-bne Ua
cas it sorption of red Hight That the HO moe
lo Nea rbd Fes in te are, which extends
stot no the sb The sorption ST vey song, o
tues a aceetunednflection of red igh a the surtace
toscas ranted and gradually absorbed Ut
deo
boat 30 m of scale, reds almost completely
oa te sul This Same proces of selective
shorron's espns or the colors af row eye and hut
Actes of bits and bes and cabges and kings Inde e
lary of objet in nature appear o have character
ol se result of preferential absorption by pement
eos n contas with most atom: and moles, which
Jan romane in the ultraviolet and fared, Ue pigment
sible pers have energie af roughly 1.6 eV 10 3.2 eV
hi yu might expect, ae on he low se for ordinary
{lest and on te high side or excitan via mo
cum m. Despite thi these
and tons he configuration ofthese sells provide
mad oo cry entation. addition. there he go
To franc dye molecules, which evideily aso have
resonances inthe visible, Al such substances, wheter nu
y conjgate system Tie acta typified by the caso
molecule Case Fi. 4.63). The erolenoids range in colt
from yellow Io re and are found in carol, tomatoes, ds
pls ar amater group of tir atra prets, batho
A ponion ofthe lng chain is tured round on el to forme
fing ln any event, conjugated system ofthis sor contain à
numberof patulry mobil letons known a pi electrons,
They are not bound o spécifie atome sites but insend cu
range over the relavely large dimensions ofthe molecu
‘hai or sng nthe prascology of Quantum Meche
ay tha these ae long-wavelength low-frequency and here
fore low-energy. elsron sates he encre required tore
à pi electron to am exited wate is comparatively low, ome
pong to ha oF visible photons. In efet te molecule cin
Imagine a an Or having «resonance HUE I
the vis,
CRT mc.
wade nn ce
tn eS eee
ace ech wanpret at when ds ech her bene
‘be paper emering rh os pr a arc bea on
wer andrgoing amero: flection tl
the dye ies. The exiting lit wil be elored oe ont
shit lacks the fuen component abr bythe ye. This
is presuely-why a Lal appears pen. or a Banana yellow
A bone odiar le ink ook Bloc neither reed
“and the savent evaporates, something aber interest hap
pe. The conceited pigment absorbs so fe it
Pack tothe dea tht a tong absorber ager) to
reflector Thus, copcentated blue gee ink eles fe
overbead projector pes ae bes). but you us se reflected
igh om below. The most convene way to accomplsh ha
ink omo 3 black alae a sey
Sorta For example, rca reia or a Wack ra
od wil lo gren in ei ig. Genta ill which
las aide and et dry in ack cout. Examine Boh the
The wbole ane of les Inch sd, en, and Dl
Biniions of magenta, cyan, and yellow filters (Fig. 165)
Bes din mak photogs an nse wp
tay coining ants ry kings you tos
Slugs beta
th ioe ajo apr ch, Tart at
RE
din une oes pa nd
reflection eco, and sep tee a rer na
tn eS eee
ace ech wanpret at when ds ech her bene
‘be paper emering rh os pr a arc bea on
wer andrgoing amero: flection tl
the dye ies. The exiting lit wil be elored oe ont
shit lacks the fuen component abr bythe ye. This
is presuely-why a Lal appears pen. or a Banana yellow
A bone odiar le ink ook Bloc neither reed
“and the savent evaporates, something aber interest hap
pe. The conceited pigment absorbs so fe it
Pack tothe dea tht a tong absorber ager) to
reflector Thus, copcentated blue gee ink eles fe
overbead projector pes ae bes). but you us se reflected
igh om below. The most convene way to accomplsh ha
ink omo 3 black alae a sey
Sorta For example, rca reia or a Wack ra
od wil lo gren in ei ig. Genta ill which
las aide and et dry in ack cout. Examine Boh the
The wbole ane of les Inch sd, en, and Dl
Biniions of magenta, cyan, and yellow filters (Fig. 165)
Bes din mak photogs an nse wp
tay coining ants ry kings you tos
Slugs beta
th ioe ajo apr ch, Tart at
RE
din une oes pa nd
reflection eco, and sep tee a rer na
ere 63 Toner mas eco tes
example, sarabuió betes mane themselves inthe brian
and waveengi depende ierteenc effects contre 1
babes, peacock, bummingbinds
4.10 The Stokes Treatment of Reflec-
tion and Refraction
bacon a a omo as Bed by e Bah
re Cabrel Soles (1819-193), Suppe
pins Sir GK
hat we have an incide wave ol amplitud Aa impingin
the planar intra separa wo delete media, ein ie
Factor amplitdes reed and tratos, respectively
[Again we are reminded hal Ferma’ Princip edo he Pi
‘Spe of Reversi, whieh es a Me son depa
Fig 6 whee ae ay Seton are reece mit
‘kobe physical powäble. With he ne rois da here be
mat be reverube. Equivalently, in te ion of moder
ne speak of time renal variance thls a
he even poses can ao orsu. Ta if we
Tikes hypotieucal motion picture ofthe wave inciden on
Favio eps wen hein run baca st alo be
There are now two incident waves of amplitudes Er amd Fat
A porn of the wave woe apse is Ei bath elect
and rante a the interac. Without making any
Ssompuions tan beth ampli flection and an
below (ie = yn, =m). Contequent. the else po
te incoming wave whose amplitee En slt into see
tents of ampliado grand Fyre. the configuration Fig
A be ential with hatin Fig 4655, then ios
Th discusion cl fora bit more caution than i ually
ranted i I must be poes ou hat te ampliade ef
example, sarabuió betes mane themselves inthe brian
and waveengi depende ierteenc effects contre 1
babes, peacock, bummingbinds
4.10 The Stokes Treatment of Reflec-
tion and Refraction
bacon a a omo as Bed by e Bah
re Cabrel Soles (1819-193), Suppe
pins Sir GK
hat we have an incide wave ol amplitud Aa impingin
the planar intra separa wo delete media, ein ie
Factor amplitdes reed and tratos, respectively
[Again we are reminded hal Ferma’ Princip edo he Pi
‘Spe of Reversi, whieh es a Me son depa
Fig 6 whee ae ay Seton are reece mit
‘kobe physical powäble. With he ne rois da here be
mat be reverube. Equivalently, in te ion of moder
ne speak of time renal variance thls a
he even poses can ao orsu. Ta if we
Tikes hypotieucal motion picture ofthe wave inciden on
Favio eps wen hein run baca st alo be
There are now two incident waves of amplitudes Er amd Fat
A porn of the wave woe apse is Ei bath elect
and rante a the interac. Without making any
Ssompuions tan beth ampli flection and an
below (ie = yn, =m). Contequent. the else po
te incoming wave whose amplitee En slt into see
tents of ampliado grand Fyre. the configuration Fig
A be ential with hatin Fig 4655, then ios
Th discusion cl fora bit more caution than i ually
ranted i I must be poes ou hat te ampliade ef
sin. Te eo equation ind
ment inne he Fresa Equation
sin. = an =
nr er us
Dera compared by sting &
an = 8 (exe
ve from Sels Lav I
a refloin), 8
below (i sino
in suis Eg (4.42) bu her is oO, as ben
some incident angle ica fre Now spore.
rain that @ = 9, Then @ = he
hoe te fi ivan, ad
vas detonate rev
Zn SRO
‘Abo i may be uneeesun ne a ont at
Te 180 phe difteence bene ech pr of componentcis
rider fig Asa, Pr Keepin mind thar when D = 84
nai wave, Eq (4.39) not aplicable andas we
tha bah ths prall nd pepe
cule components ofthe extemal ect Beam change
{oes mo phe shift al, Ths que income
4.11 Photons, Waves,
and Probability
theoreti gounding of Opie ie pres
and that i's ea À one example ou of he
ecommerce, the pres sain sn
ment inne he Fresa Equation
sin. = an =
nr er us
Dera compared by sting &
an = 8 (exe
ve from Sels Lav I
a refloin), 8
below (i sino
in suis Eg (4.42) bu her is oO, as ben
some incident angle ica fre Now spore.
rain that @ = 9, Then @ = he
hoe te fi ivan, ad
vas detonate rev
Zn SRO
‘Abo i may be uneeesun ne a ont at
Te 180 phe difteence bene ech pr of componentcis
rider fig Asa, Pr Keepin mind thar when D = 84
nai wave, Eq (4.39) not aplicable andas we
tha bah ths prall nd pepe
cule components ofthe extemal ect Beam change
{oes mo phe shift al, Ths que income
4.11 Photons, Waves,
and Probability
theoreti gounding of Opie ie pres
and that i's ea À one example ou of he
ecommerce, the pres sain sn
infec ahs pour ascended ol ca
ater pe er onto
¡Chapo 9)-Iftvo of more clecromagnei waves ative at
Dein ot opine and ancl, "What does ht mean far
ir ny teconscme? Energy can broca bat
does cancel out We ve learned from Quantum Mecha
othe mos andere
fs hata base irren on
‘Remembering Elis admonition hat tere ar no
Teal nan
ration ofthe clasica wavs eld. Alter
its continuos distribucion of energy does nt setually exist.
Paap we soa hk oF he wave a The CI par
ere pace ater ha being va wave field a e
Wonderuly cuna tlle ware ths
teas of calling he macroscopic diront
For example cons
y he radiance on a ren place fr
ysis
yayo deso compared
Suppose ihnen al obaring ie ae
Saphir allo by aph
ES RISK ER U
‘ach location, N Taking ret many sich messurement,
pai discuto ofthe number of poten count wool
would be ofthe very same form a tha for he
ramely M8 = Mine B/0 the number pl
to tected ls proportional othe radiance, A soumabe
{ak aba the probably of dic photo at any pin on
the sree, Thats probsbiltydsibaton can be comet.
ft rmiiacent of Fig, 223. Beaute he pacs variables
or) nc contin >t indes a probabil
ity den er be 4.9) Then 919, 40 the probably a
‘phon ml e fon inthe niteimal range fom 90 9
The square healer sé amplitud avr po
RENE canbe ced
Ai). and ar alsa lo Acond a ing
probability amplitude asar quay whose ao value
rare qi the probably demi Ts te et Eat
Lan be interpreted bins proponional 1 à semielasea
probability anpinude inasmuch the probabil of detecting
{photon a some point in space depends one radiance ot
‘ar location and, Thins in cord mth Entei com
on hs ight ici, which Max Bom (bo init the
‘stitial interpreta of Quantum Mechanic described as
tha eld eve how the photons distribu in spac in ie
tle somehow relates tothe probability deny of rin
hom I he fra weiment of Quantum Mactan the
probable is generale any hs
Ahle vali quae comespond tothe probably denis
Lee Schrager avai a probably aap
Jude). Thus, However resonable 1 was lo onside Ey a
‘Sone crie over. to quantum cry
proves, unsere. im ems of probable, anche br for
‘eof the probable amplitude fort takin
rada
ater pe er onto
¡Chapo 9)-Iftvo of more clecromagnei waves ative at
Dein ot opine and ancl, "What does ht mean far
ir ny teconscme? Energy can broca bat
does cancel out We ve learned from Quantum Mecha
othe mos andere
fs hata base irren on
‘Remembering Elis admonition hat tere ar no
Teal nan
ration ofthe clasica wavs eld. Alter
its continuos distribucion of energy does nt setually exist.
Paap we soa hk oF he wave a The CI par
ere pace ater ha being va wave field a e
Wonderuly cuna tlle ware ths
teas of calling he macroscopic diront
For example cons
y he radiance on a ren place fr
ysis
yayo deso compared
Suppose ihnen al obaring ie ae
Saphir allo by aph
ES RISK ER U
‘ach location, N Taking ret many sich messurement,
pai discuto ofthe number of poten count wool
would be ofthe very same form a tha for he
ramely M8 = Mine B/0 the number pl
to tected ls proportional othe radiance, A soumabe
{ak aba the probably of dic photo at any pin on
the sree, Thats probsbiltydsibaton can be comet.
ft rmiiacent of Fig, 223. Beaute he pacs variables
or) nc contin >t indes a probabil
ity den er be 4.9) Then 919, 40 the probably a
‘phon ml e fon inthe niteimal range fom 90 9
The square healer sé amplitud avr po
RENE canbe ced
Ai). and ar alsa lo Acond a ing
probability amplitude asar quay whose ao value
rare qi the probably demi Ts te et Eat
Lan be interpreted bins proponional 1 à semielasea
probability anpinude inasmuch the probabil of detecting
{photon a some point in space depends one radiance ot
‘ar location and, Thins in cord mth Entei com
on hs ight ici, which Max Bom (bo init the
‘stitial interpreta of Quantum Mechanic described as
tha eld eve how the photons distribu in spac in ie
tle somehow relates tothe probability deny of rin
hom I he fra weiment of Quantum Mactan the
probable is generale any hs
Ahle vali quae comespond tothe probably denis
Lee Schrager avai a probably aap
Jude). Thus, However resonable 1 was lo onside Ey a
‘Sone crie over. to quantum cry
proves, unsere. im ems of probable, anche br for
‘eof the probable amplitude fort takin
rada
mues A qantanmechanial methodology enslogoscto ie
inthe con after development of Quant Escoiynan
In bee, cial obser autom of mo de:
‘cd by he Soperponon of all the vario probably
he event cum occur Inother mor cach route" along which
et malena oprsntntiona.omplex postal
ade. Al ofthese ten comic — and intros as com
What follows iy a rea sip!
cd ver
4.11.1 QED
Feynman was rater unequivocal in ie anes regarding
sie of igh
sought: its a steam of photons hose behavior en ase
cine determined sataicaly For exampie 10 pon
je wil bo rellectd achat from the fr sure hey
outer. Which cannot be known, and infact how those
Funicla à photons ae selected I a mystery. What canbe
iced an confirmed experimental hat 45 of in
RIVA be rte (p27)
eo rls, withthe uit juin big hat wor:
scheme makes accurate predictions (1) The probability
ampildeestecired withthe occurrence of om event the
‘oof he constituent probably amplitudes correspond.
Ant cach and every possible wos he event con occur D)
ich such constituent probably ampliado i general
‘apresibleasacompler quan. Rater han araycally
mini these consten! probability ampltuos we san
(3) The probability of ccurrence of he event os a hole is
proportional able square of thereat proba
"We can apprenons comes wg byw
gi recon picture im ig. AT pi are Sl
familiar ave model. canbe ane a analogue topnaide
Rete 67 à sete nen Ang
inthe con after development of Quant Escoiynan
In bee, cial obser autom of mo de:
‘cd by he Soperponon of all the vario probably
he event cum occur Inother mor cach route" along which
et malena oprsntntiona.omplex postal
ade. Al ofthese ten comic — and intros as com
What follows iy a rea sip!
cd ver
4.11.1 QED
Feynman was rater unequivocal in ie anes regarding
sie of igh
sought: its a steam of photons hose behavior en ase
cine determined sataicaly For exampie 10 pon
je wil bo rellectd achat from the fr sure hey
outer. Which cannot be known, and infact how those
Funicla à photons ae selected I a mystery. What canbe
iced an confirmed experimental hat 45 of in
RIVA be rte (p27)
eo rls, withthe uit juin big hat wor:
scheme makes accurate predictions (1) The probability
ampildeestecired withthe occurrence of om event the
‘oof he constituent probably amplitudes correspond.
Ant cach and every possible wos he event con occur D)
ich such constituent probably ampliado i general
‘apresibleasacompler quan. Rater han araycally
mini these consten! probability ampltuos we san
(3) The probability of ccurrence of he event os a hole is
proportional able square of thereat proba
"We can apprenons comes wg byw
gi recon picture im ig. AT pi are Sl
familiar ave model. canbe ane a analogue topnaide
Rete 67 à sete nen Ang
140. Chapter 4 The Posse li
ig an esh of which sants possible path
there are à nuit of pats, but the several we have drawn
athe apte (Ea) and phase of ach such wavelet a P
willen he esla! ampliado AS wesw wih
the mim to Peach th pase ofeach wavelet rv
1 PeMorcowr the greater he pu Length e more D
x. 4
gure 468 la of he OPL with minimum tt
tage phase dference and à comespontingy ng wen
sheplnson drawn in Fig 468 Going from Ate Bw Cand
‘nd cach por la th previo one by malle angle ot
By the spe of he cuve) effec. de nor ta the el!
reste comercios fom 11 Since OPLI a e
mot pies rm tg ee lp ilies
Hein ph ange Ging from oJ Kandaoon 00,0%
han 1 he ip of rote clockwise om 710.
In Fig. 468 the rest amplitud e dea fom te
Abe ne els ed amplitude at 2, The iradiance is pre
Paronal the square fe ne ed amie, and ba,
ram shouldbe a mestre of the ikcibood o ding a po
Fat move hayon he la ideas of etc wave
ra ii paths. Us reasonable to asume hat ech sh
sath kes a poi cotas e end rel an exon
Engl long ote out oh sry edge the sro and back
Should online from than a mote isst route. Fk
pres quanti, constituent quantum mechanical (QM
probabilisampltude wit cach posse path Esc such
arte QM probity amplia an be represented e
par lg avec (Of cour, hiss jos what obriod
eh puso 1 Fig 468 Stl hee ae coming ne
“ony th lanical fe anno o the OM probability
pide) Thott QM probable he sm ot
al such phsrscomespooding 1 al possible pa an thats
‘Now sli Fig. #68 50 thi represents the quantum
mechanical formation Clay mon of the Teng of the
resultan QM probability amplitude arses from contribu
tons tn the immediate vein of path SI, where the eon
Stem phasor are large and nearly phase. Mos of
ig an esh of which sants possible path
there are à nuit of pats, but the several we have drawn
athe apte (Ea) and phase of ach such wavelet a P
willen he esla! ampliado AS wesw wih
the mim to Peach th pase ofeach wavelet rv
1 PeMorcowr the greater he pu Length e more D
x. 4
gure 468 la of he OPL with minimum tt
tage phase dference and à comespontingy ng wen
sheplnson drawn in Fig 468 Going from Ate Bw Cand
‘nd cach por la th previo one by malle angle ot
By the spe of he cuve) effec. de nor ta the el!
reste comercios fom 11 Since OPLI a e
mot pies rm tg ee lp ilies
Hein ph ange Ging from oJ Kandaoon 00,0%
han 1 he ip of rote clockwise om 710.
In Fig. 468 the rest amplitud e dea fom te
Abe ne els ed amplitude at 2, The iradiance is pre
Paronal the square fe ne ed amie, and ba,
ram shouldbe a mestre of the ikcibood o ding a po
Fat move hayon he la ideas of etc wave
ra ii paths. Us reasonable to asume hat ech sh
sath kes a poi cotas e end rel an exon
Engl long ote out oh sry edge the sro and back
Should online from than a mote isst route. Fk
pres quanti, constituent quantum mechanical (QM
probabilisampltude wit cach posse path Esc such
arte QM probity amplia an be represented e
par lg avec (Of cour, hiss jos what obriod
eh puso 1 Fig 468 Stl hee ae coming ne
“ony th lanical fe anno o the OM probability
pide) Thott QM probable he sm ot
al such phsrscomespooding 1 al possible pa an thats
‘Now sli Fig. #68 50 thi represents the quantum
mechanical formation Clay mon of the Teng of the
resultan QM probability amplitude arses from contribu
tons tn the immediate vein of path SI, where the eon
Stem phasor are large and nearly phase. Mos of
secumulted probability fo light ogo from to Pv fe
kon stes along and inmedinely adjacent o pak LP The
regions a end of the mir combat very tle bene
the phator fom those arts form tight spirale at bom
esremes (Fig 468), Covering the nds ofthe mir will
iheefoe litle afec on the amount of ight reashing P- Keep
in mind that this diagram ater cade inca 1 oun
fom 81 P these are Blas of pose pt. ande ps
‘QED predicts that ie emited by a point source reflets
‘ut oP rom al aan he mor ut it he OS Ry
owe is S-.inwhish case À = 8 With som eye st P look
fag in the nino, you es one sary mage of
4.11.2 Photons and the Laws of Reflection
and Refraction
‘cane such quantum hat ses the intrface between m0.
dete media (et and hos at an angle 9, Tat pho
tunis absorbed by a atone Fhe glass and anidemica
hati hs wer just ne out bilans o such ants as
row Inerbeam. oui conform o Sels Law. To explore
this behavior les examine he dynamics sociated with he
Brand so vector momenta mos be o
Bonk
ere ithe propagation vector and 2. Cent
Iytheinsident and ranmited mamena ate 6 — Ak ad
PROBLEMS
component of momentum perpendicular othe nee e
leaves se parallel component unchanged, Indeed, we know
experimentally ha ear momcmem perde ot
interface cam be amer 1 a medium from a ha ba
(Section 338) The tement coneraion of he compo,
ren o momentum parallel 1th tec or asia lt:
We are at an pont juncture here: SCD Ue
moment ofa mata ale depends cai sped Wen.
in follows (or he Ses Law an the above qua
on thi =p he pate of Hg must presi
sped up. Indes, he fis dan of he Lan o Rett
online by Rene Descartes (1697, wrongly tested ight
strc of pres that sped ep an I entered the ott
‘more deme medium (se Problem 31) By cast th fist
entered more dense medium wa probably Thomas Young
ISO. Be ih infeed at the speed of igh em
‘as thereby aa reduced =
We nos Leow fom Quantum Mechanics that th spel of
a photo i always nd ha is momento depends on it
RE ans ni tsp Th
Malin bot sides by c/s we get Sols Law
biti appling pedagogy
kon stes along and inmedinely adjacent o pak LP The
regions a end of the mir combat very tle bene
the phator fom those arts form tight spirale at bom
esremes (Fig 468), Covering the nds ofthe mir will
iheefoe litle afec on the amount of ight reashing P- Keep
in mind that this diagram ater cade inca 1 oun
fom 81 P these are Blas of pose pt. ande ps
‘QED predicts that ie emited by a point source reflets
‘ut oP rom al aan he mor ut it he OS Ry
owe is S-.inwhish case À = 8 With som eye st P look
fag in the nino, you es one sary mage of
4.11.2 Photons and the Laws of Reflection
and Refraction
‘cane such quantum hat ses the intrface between m0.
dete media (et and hos at an angle 9, Tat pho
tunis absorbed by a atone Fhe glass and anidemica
hati hs wer just ne out bilans o such ants as
row Inerbeam. oui conform o Sels Law. To explore
this behavior les examine he dynamics sociated with he
Brand so vector momenta mos be o
Bonk
ere ithe propagation vector and 2. Cent
Iytheinsident and ranmited mamena ate 6 — Ak ad
PROBLEMS
component of momentum perpendicular othe nee e
leaves se parallel component unchanged, Indeed, we know
experimentally ha ear momcmem perde ot
interface cam be amer 1 a medium from a ha ba
(Section 338) The tement coneraion of he compo,
ren o momentum parallel 1th tec or asia lt:
We are at an pont juncture here: SCD Ue
moment ofa mata ale depends cai sped Wen.
in follows (or he Ses Law an the above qua
on thi =p he pate of Hg must presi
sped up. Indes, he fis dan of he Lan o Rett
online by Rene Descartes (1697, wrongly tested ight
strc of pres that sped ep an I entered the ott
‘more deme medium (se Problem 31) By cast th fist
entered more dense medium wa probably Thomas Young
ISO. Be ih infeed at the speed of igh em
‘as thereby aa reduced =
We nos Leow fom Quantum Mechanics that th spel of
a photo i always nd ha is momento depends on it
RE ans ni tsp Th
Malin bot sides by c/s we get Sols Law
biti appling pedagogy
146 chapters
5.1 Introductory Remarks
tal late bebaves a Fü consid of a very I
vo. Ut in in he direction ofthe Poynting sector In ti
se be converting. Generali. ane deals oy à
no porn à avetont À point from which a portion of
oleo wane diverges, ca tome tick te neve Se
Dent converges, is known as a focus of the bundle of ray
igus .1 deics a pot source fn the viii of some
a api sytem. OF te inti of rays emanating foma.
hme ays 1 ave ate era point 7, aia Fg Si
trough the system ai vo estigma
ses two pins, The energy ite cone apar fom
ces P which is then refered o as a perfect image ofS.
Te wave coud conceTvably arrive Crm Tne pach of
Ica ote Pee Revenant 110) tt
‘ad coin} the wo ate spoken fa conjugate point.
ian deal optica sem every point fs ce dimcnonat
Geometrical
Optics
regis, the former being the objet space, the ace the
Most commonly te fun
{hein purpose ol forming an mago ofan objet Note
‘at inherent in ealiabl ste he mon of eine
‘abl to collect all he emited light a system generally
epi ony a opment of the wavefront. As sul fee wll
Away be an apparent deviation fro recliner propagación
ten in homapeneons edith waves wil be fie,
m willbe diran (here al ass be ler
‘in comparison tepic! mensions ofthe ob
tem ie effect of diffraction become lee ini
Geometrical Optics Behavior tat pial att
leo he wave tre of ah ep, rence and ii
rm the aprosimation of Goo
rain efec
fronts or ry by means of the inep
ws agus mer
tal late bebaves a Fü consid of a very I
vo. Ut in in he direction ofthe Poynting sector In ti
se be converting. Generali. ane deals oy à
no porn à avetont À point from which a portion of
oleo wane diverges, ca tome tick te neve Se
Dent converges, is known as a focus of the bundle of ray
igus .1 deics a pot source fn the viii of some
a api sytem. OF te inti of rays emanating foma.
hme ays 1 ave ate era point 7, aia Fg Si
trough the system ai vo estigma
ses two pins, The energy ite cone apar fom
ces P which is then refered o as a perfect image ofS.
Te wave coud conceTvably arrive Crm Tne pach of
Ica ote Pee Revenant 110) tt
‘ad coin} the wo ate spoken fa conjugate point.
ian deal optica sem every point fs ce dimcnonat
Geometrical
Optics
regis, the former being the objet space, the ace the
Most commonly te fun
{hein purpose ol forming an mago ofan objet Note
‘at inherent in ealiabl ste he mon of eine
‘abl to collect all he emited light a system generally
epi ony a opment of the wavefront. As sul fee wll
Away be an apparent deviation fro recliner propagación
ten in homapeneons edith waves wil be fie,
m willbe diran (here al ass be ler
‘in comparison tepic! mensions ofthe ob
tem ie effect of diffraction become lee ini
Geometrical Optics Behavior tat pial att
leo he wave tre of ah ep, rence and ii
rm the aprosimation of Goo
rain efec
fronts or ry by means of the inep
ws agus mer
The lens o doubt the most wie une optical devise and
tars not even consider the fact ha we se the word
to the buring lanes of antiquity. which, as be mame
Sips, were ued o ir fies Tong before the advent of
riches. In mos general ter, let fs a retracting,
cconfiguecs a transmitted energy distribution That much
‘rue whether we are dealing with UV. line, IR
‘esting ofthe wavelton tis designed 0 perform, Point
ours arbi, bd o fon dele to conver diver
eam from spreading ot and weakening 3 prog
sine revere, quel neewany I collet
Tens: Moreover. sige db tight ect fom someone's face
If point vous ens hat ca
5.2.1 Aspherical Surfaces
‘ferent than was nly Fig as across se
Pre 52 home de
tars not even consider the fact ha we se the word
to the buring lanes of antiquity. which, as be mame
Sips, were ued o ir fies Tong before the advent of
riches. In mos general ter, let fs a retracting,
cconfiguecs a transmitted energy distribution That much
‘rue whether we are dealing with UV. line, IR
‘esting ofthe wavelton tis designed 0 perform, Point
ours arbi, bd o fon dele to conver diver
eam from spreading ot and weakening 3 prog
sine revere, quel neewany I collet
Tens: Moreover. sige db tight ect fom someone's face
If point vous ens hat ca
5.2.1 Aspherical Surfaces
‘ferent than was nly Fig as across se
Pre 52 home de
hun of index impiaing on be cured interac of
rame mediar of Index n- When ns restr an
ct medium, These extremis overtake the midregion. con.
cpu, the spheica wavelrot Bend ino a plane wav.
The aemaive a representation i shown tn Fg 8.3; he
Der dense medium. and ce surface configuration e us
Ai be ays ees paral
To nd the required shape of he imrfce, eer o Fig
Seti pla A calle any here on he boundary. One
sneer i anse ino another, provided he path
A which the energy propagates are al equal" hereby
"anny te ple of fe wavefont(p. 20 À hile sper
Ena srta o conse pase at DD. Whatever pth tight
es rom So DD tus always be te same umher of
‘Shien long, o a he distance begins and end
fie Radian energy leaving Sas a singe wavefont most
{Seat the plane DD having tale or he sare aunt
ny paricula yn aer werds FA/A, the rae oF
seavelengt along the array ay rom 74) pas D/A,
number of eavlenihe along de y Hm A 0 D mst
be conti regardless of whee on the Ira A apps
mA + n, QD) = constan €
Each em anti tie en aveo in mou
eats the optical pat eng OPL tases. The Opi path
enr om to DD ae al equal 1 E 1) ised hs
the int erm becomes the tine takes ight ave! rom So
‘Nand the second te, theme from Ato we ich side
tion (31) equivalent saying that all paths fom So DO
ie ih ame amount time o aves
Lars etn ding te ape the inter, DNAS Fi
FA + [AD = cons 62
This st equation of» hyperbola im which the ce
Am) > kta is e = my > The peer the een
Source is lated at he focus, and he interface betwee he
In media is hyperbol, plan waves are santino Be
her ex ater Ws el for Problem Jo sab at
when (n/n) 1. the imerface muse be ellipsoidal ln each
ae acted in Fig 54. ery cer vege fom o cor
Nee toward foal point. Fuhermore the ys ca Be
reversed otha hey tel either way plane wave Inc
ie NE
Fire 54. ed pet nd and on
rame mediar of Index n- When ns restr an
ct medium, These extremis overtake the midregion. con.
cpu, the spheica wavelrot Bend ino a plane wav.
The aemaive a representation i shown tn Fg 8.3; he
Der dense medium. and ce surface configuration e us
Ai be ays ees paral
To nd the required shape of he imrfce, eer o Fig
Seti pla A calle any here on he boundary. One
sneer i anse ino another, provided he path
A which the energy propagates are al equal" hereby
"anny te ple of fe wavefont(p. 20 À hile sper
Ena srta o conse pase at DD. Whatever pth tight
es rom So DD tus always be te same umher of
‘Shien long, o a he distance begins and end
fie Radian energy leaving Sas a singe wavefont most
{Seat the plane DD having tale or he sare aunt
ny paricula yn aer werds FA/A, the rae oF
seavelengt along the array ay rom 74) pas D/A,
number of eavlenihe along de y Hm A 0 D mst
be conti regardless of whee on the Ira A apps
mA + n, QD) = constan €
Each em anti tie en aveo in mou
eats the optical pat eng OPL tases. The Opi path
enr om to DD ae al equal 1 E 1) ised hs
the int erm becomes the tine takes ight ave! rom So
‘Nand the second te, theme from Ato we ich side
tion (31) equivalent saying that all paths fom So DO
ie ih ame amount time o aves
Lars etn ding te ape the inter, DNAS Fi
FA + [AD = cons 62
This st equation of» hyperbola im which the ce
Am) > kta is e = my > The peer the een
Source is lated at he focus, and he interface betwee he
In media is hyperbol, plan waves are santino Be
her ex ater Ws el for Problem Jo sab at
when (n/n) 1. the imerface muse be ellipsoidal ln each
ae acted in Fig 54. ery cer vege fom o cor
Nee toward foal point. Fuhermore the ys ca Be
reversed otha hey tel either way plane wave Inc
ie NE
Fire 54. ed pet nd and on
den rs he igh om he imtrtce ni Se wi com
ver of othe eat the farts focos ofthe elisa
dana abe ga en far withthe ea without Sel’ Law.
‘Onc tat elton was discover, Desc 1657) using
hs Anal Gruey could develop the theres eda
(ont the opis of aspherical surfaces The anal pen.
flee win Gene a gif fino Descartes.
Ws an on mar now 1 comas Tec sch that ho
eh) wil be atid of the msm ofthe kn In Fig. 55
at the fit mac via the mecheniam of Fi, Ste. Tse
plans waves within lens srk the back face pempendcular
Yan emerge unre: @ = 0 and, 0. Becas the ays
yo reerable, pla ases coming ro he ih o
Fp oni fat Facet the paral! ays rom ie Sur,
Both of thes lose at ler as het mio han tee
ls snd ar therfore sido Be comen rom be Latino
to comer Rome. Ren aM more toward he coal
A cree, they are ler 1 35 comverginglenss.
contrat, a concave lens (rom the Lath conca
ges, os inevident in Fig 85 cause try ta nr as
Parallel bundle to diver. All such device hat rn ry
tard away fromthe conta ans and 5 doing a iver
sens o ie beam) are called diverging lenses. In Pig 5 Sc
‘When a paral! bundle of ray passes through a conver
‘hough a diverging lens, the point rom which diversen)
ina focal pit othe es,
Aa oia sure i positioned on he cent o optical ais
source woul appear seeen peed sm imag ts
therfore said te real. On teeter hand. in Fig. § Se
point source st init. al he ys meting fom the ss
tem is tm are diverging. They aparto com from a oi
ha tein. The image here spoken fas virtual a 1
‘psi clemente lenses and itor) of the ar we hae
kl about
with one or both surfaces neither parut
‘ion is easy to understand and they perform certain tasks
reat accuracy. Nopetcless, where the costs are justifiable:
the require precision not esting or the volume produc
age enough. aspherics uc beng used and will surly have
DD”
Fine 58 101 a Sr pote mes ss h uns
ver of othe eat the farts focos ofthe elisa
dana abe ga en far withthe ea without Sel’ Law.
‘Onc tat elton was discover, Desc 1657) using
hs Anal Gruey could develop the theres eda
(ont the opis of aspherical surfaces The anal pen.
flee win Gene a gif fino Descartes.
Ws an on mar now 1 comas Tec sch that ho
eh) wil be atid of the msm ofthe kn In Fig. 55
at the fit mac via the mecheniam of Fi, Ste. Tse
plans waves within lens srk the back face pempendcular
Yan emerge unre: @ = 0 and, 0. Becas the ays
yo reerable, pla ases coming ro he ih o
Fp oni fat Facet the paral! ays rom ie Sur,
Both of thes lose at ler as het mio han tee
ls snd ar therfore sido Be comen rom be Latino
to comer Rome. Ren aM more toward he coal
A cree, they are ler 1 35 comverginglenss.
contrat, a concave lens (rom the Lath conca
ges, os inevident in Fig 85 cause try ta nr as
Parallel bundle to diver. All such device hat rn ry
tard away fromthe conta ans and 5 doing a iver
sens o ie beam) are called diverging lenses. In Pig 5 Sc
‘When a paral! bundle of ray passes through a conver
‘hough a diverging lens, the point rom which diversen)
ina focal pit othe es,
Aa oia sure i positioned on he cent o optical ais
source woul appear seeen peed sm imag ts
therfore said te real. On teeter hand. in Fig. § Se
point source st init. al he ys meting fom the ss
tem is tm are diverging. They aparto com from a oi
ha tein. The image here spoken fas virtual a 1
‘psi clemente lenses and itor) of the ar we hae
kl about
with one or both surfaces neither parut
‘ion is easy to understand and they perform certain tasks
reat accuracy. Nopetcless, where the costs are justifiable:
the require precision not esting or the volume produc
age enough. aspherics uc beng used and will surly have
DD”
Fine 58 101 a Sr pote mes ss h uns
‘ees ae later and ger han regular phil ones Ax
sad ey 10 well ited foro precio Fuimos
x oer people
“ph generators, x producing elements with tolerances
Tie depart fom the died surface) of be han OS
Jam (0.000020 inc Thine il about factor of 10 uy
fee general required tolerance of or quality optic.
Ale gindig,apheres ca be polished ngnctorhclogcal
iy Ths echaige, used wo figure and Gis the ara, mag
al controls the decos ed prone applied io te
"choc y the abrasive particles during posing.
‘Nowadays aspheri made in plat and glas can D found
inal Kind of instruments aros the whole ange of qual
cig NEO popes ER ad SR
52.2 Refraction at Spherical Surfaces
er acompte both ring de noc rd
‘Sa nique property ofthe sphere hat such pieces wil fit
Tf we tk wo oughly spherical objet ol stable cur
52 Lee 153
arte tem with some abrasive and then randomly
high spots on either objet wil wea away, Asıhey wear, oth
Eurfaces are commonly generated in batches By autom
‘Not surprisingly. the vast majority of quality lenses in use
today have surfaces that are sgment of sphere. Our tent
here to sabi techniques or ing mich faces ima
taneously mage à great many objet ains night composed
fof trou ang frequencies, Image ero known a abe
ations wl cor, but posbl wth he presen tc
shenationsafesowellconoled hat age Rey md
Figure 56 depict a wave fromthe point souse Spine
po Vi alle vertex of th surface: Te lengths, = SV
know as e abject distance Then SA wil e reco
fore twa the central optical al. Accum tha a sone
à ar
sad ey 10 well ited foro precio Fuimos
x oer people
“ph generators, x producing elements with tolerances
Tie depart fom the died surface) of be han OS
Jam (0.000020 inc Thine il about factor of 10 uy
fee general required tolerance of or quality optic.
Ale gindig,apheres ca be polished ngnctorhclogcal
iy Ths echaige, used wo figure and Gis the ara, mag
al controls the decos ed prone applied io te
"choc y the abrasive particles during posing.
‘Nowadays aspheri made in plat and glas can D found
inal Kind of instruments aros the whole ange of qual
cig NEO popes ER ad SR
52.2 Refraction at Spherical Surfaces
er acompte both ring de noc rd
‘Sa nique property ofthe sphere hat such pieces wil fit
Tf we tk wo oughly spherical objet ol stable cur
52 Lee 153
arte tem with some abrasive and then randomly
high spots on either objet wil wea away, Asıhey wear, oth
Eurfaces are commonly generated in batches By autom
‘Not surprisingly. the vast majority of quality lenses in use
today have surfaces that are sgment of sphere. Our tent
here to sabi techniques or ing mich faces ima
taneously mage à great many objet ains night composed
fof trou ang frequencies, Image ero known a abe
ations wl cor, but posbl wth he presen tc
shenationsafesowellconoled hat age Rey md
Figure 56 depict a wave fromthe point souse Spine
po Vi alle vertex of th surface: Te lengths, = SV
know as e abject distance Then SA wil e reco
fore twa the central optical al. Accum tha a sone
à ar
154 Chapt Genis
¡Genta the sane ange Fig 5.2). The length = VPs the
Image distance Fermat's Principle maintains that he opal
pathlength OPE wile stationary at deriva with
{expect 0 the poi variable wil be eno. Por e ray in
‘weston,
sing he aw of cosines in wanes SACAN ACP along with
AO AO 9). We BEL
C= HP + (+ RP = ay + Rense
|
“The OPL can be rewsten as
OPL = ml + (5, + RP = Du, + B08
EAE EG = RPE RG, = ren,
‘umber, and these fom te basis fa sin convention which
is roll unfolding and 10 which we sal etu time and
Ara oe Tate $.) Inasmuch ashe poin moves athe
‘dot aimer ie, À conan, eee pay an
‘he and has sting dOPL)/de = 0, ia Fermat's Pile
TABLE 5.1 Sign Convention for Spherical
Refracting Surfaces and Thin Lenses*
(Light Entering from the Left
nfs. Rising EA
from which it follows that
ee hero hat must ol among the parameter
Fors ay going rum Sto hy way of fraction al the oben
‘complicated. If is moved toa new location by changing 6
ne en ray wil not reg the pl ais Se Prob.
Jem ct concerning the Caesar oval which i the mera
‘sonfiguation a woud ring any tay, etes of, 0 P)
thereby simply Eq (3), are rua in al that st alow
Recall hat
‘Consequently. the expressions for, end fied 4,4
‘o> avant ha approximation
a... ss
Ave cota have sum hic ceriation with Sel Las rate
thin Fermat's Principle (Problem 53), in wich case small
vales of ¢ would hve led to sia e = y and Eq (3.8) once
ses, This approxi
delineates the domain of what
em à — gite next chapter Rays tat ative at shale
Tow angles with respect othe optical xs (ch that and à
are appropriately umal) ae known as parasil ray, The
mers wavefront segment corresponding to thes a
Fui essay spherical and wil form epee" mage
ttitscener located ex, Notice that E (38's indepen
<entof the lection FA over mail arn about the syrmctry
¡Genta the sane ange Fig 5.2). The length = VPs the
Image distance Fermat's Principle maintains that he opal
pathlength OPE wile stationary at deriva with
{expect 0 the poi variable wil be eno. Por e ray in
‘weston,
sing he aw of cosines in wanes SACAN ACP along with
AO AO 9). We BEL
C= HP + (+ RP = ay + Rense
|
“The OPL can be rewsten as
OPL = ml + (5, + RP = Du, + B08
EAE EG = RPE RG, = ren,
‘umber, and these fom te basis fa sin convention which
is roll unfolding and 10 which we sal etu time and
Ara oe Tate $.) Inasmuch ashe poin moves athe
‘dot aimer ie, À conan, eee pay an
‘he and has sting dOPL)/de = 0, ia Fermat's Pile
TABLE 5.1 Sign Convention for Spherical
Refracting Surfaces and Thin Lenses*
(Light Entering from the Left
nfs. Rising EA
from which it follows that
ee hero hat must ol among the parameter
Fors ay going rum Sto hy way of fraction al the oben
‘complicated. If is moved toa new location by changing 6
ne en ray wil not reg the pl ais Se Prob.
Jem ct concerning the Caesar oval which i the mera
‘sonfiguation a woud ring any tay, etes of, 0 P)
thereby simply Eq (3), are rua in al that st alow
Recall hat
‘Consequently. the expressions for, end fied 4,4
‘o> avant ha approximation
a... ss
Ave cota have sum hic ceriation with Sel Las rate
thin Fermat's Principle (Problem 53), in wich case small
vales of ¢ would hve led to sia e = y and Eq (3.8) once
ses, This approxi
delineates the domain of what
em à — gite next chapter Rays tat ative at shale
Tow angles with respect othe optical xs (ch that and à
are appropriately umal) ae known as parasil ray, The
mers wavefront segment corresponding to thes a
Fui essay spherical and wil form epee" mage
ttitscener located ex, Notice that E (38's indepen
<entof the lection FA over mail arn about the syrmctry
noun as first-order, prasia, or Gaussian Optic, lt soon.
became he bai theoretical on y which lens would he
su corto, an incident spherical wave wil merge ia
on ery loc resembling aapbeial nave Concent,
ache petectan of te sem acres. mare close
macho it ode hor. Devito rom at of para
‘Malai will provide acoavenient mesure ofthe quality of
Te poi Fin Fig. 58s imaged at init, = 9, we
wir
‘ete jet fea length», = so Rat “
he pont Fi known se fst robot oc, Similar
Fare 39.
‘RG 510), Anas. an object viral when the aye
converge toward (ig. 5.11), Observe Wa the vil obje
len megas quit Moreover De tvfoe iron
and radis wil ale e negative, a required by Eq, (59.
became he bai theoretical on y which lens would he
su corto, an incident spherical wave wil merge ia
on ery loc resembling aapbeial nave Concent,
ache petectan of te sem acres. mare close
macho it ode hor. Devito rom at of para
‘Malai will provide acoavenient mesure ofthe quality of
Te poi Fin Fig. 58s imaged at init, = 9, we
wir
‘ete jet fea length», = so Rat “
he pont Fi known se fst robot oc, Similar
Fare 39.
‘RG 510), Anas. an object viral when the aye
converge toward (ig. 5.11), Observe Wa the vil obje
len megas quit Moreover De tvfoe iron
and radis wil ale e negative, a required by Eq, (59.
196 Chapter 5 Gnome Ones
5.2.3 Thin Lenses
Lenses ae aden a wide rane of forms; or example. tere
‘ters re far more sul in appearance se phot), Most
‘tena lens hs wo or more refracting metaces, anda ett
of thexe curved. Generali the nonplanar surfaces are
ent and are ote coated with in diese
men (hic has only 10
racing surface). spleen, The presence mor th
Fed avt
faces. Under ee tion, the simple k
forms shown ig 5.12
Lenses tata variously known as conve, converging or
if re thicker ate enter and so tnd 10 decrease
fads o curvature of he wait. nother wens the
isiminesed Concase diverging. omega lense,
on the mern, causing eto diverge mow than
an take he
“Tiens Equations
Rerun 0 the dicen
retraction a sng
[Ace cree y moves Aa evenevas Fa
and @ crane un fal = Fand «= 2 A tht pon
= (nr MR, ba, gt ans smaller.» wi hae
‘becomes ia SIR,
Wessel
Far
Sos se ee
BoC ...os
awe 512 Ci aie aa. ted ger ie
5.2.3 Thin Lenses
Lenses ae aden a wide rane of forms; or example. tere
‘ters re far more sul in appearance se phot), Most
‘tena lens hs wo or more refracting metaces, anda ett
of thexe curved. Generali the nonplanar surfaces are
ent and are ote coated with in diese
men (hic has only 10
racing surface). spleen, The presence mor th
Fed avt
faces. Under ee tion, the simple k
forms shown ig 5.12
Lenses tata variously known as conve, converging or
if re thicker ate enter and so tnd 10 decrease
fads o curvature of he wait. nother wens the
isiminesed Concase diverging. omega lense,
on the mern, causing eto diverge mow than
an take he
“Tiens Equations
Rerun 0 the dicen
retraction a sng
[Ace cree y moves Aa evenevas Fa
and @ crane un fal = Fand «= 2 A tht pon
= (nr MR, ba, gt ans smaller.» wi hae
‘becomes ia SIR,
Wessel
Far
Sos se ee
BoC ...os
awe 512 Ci aie aa. ted ger ie
‘ove tha the ys om Po shat are an indeed nich
sien onthe ot and heron poss = fk and,
Ta he eco SHY ies
ers > 2 and Ry < 0.00 tha th et hand ies pa
ine Adding Ey (31d 5. neh
a 14) nd
ren am co hs tem hei
ave the very useful Thin-Lems Equation, often refered tu
1,1 La x
se wt i y= Te pois V a Ve
eo se
Je compat the foc Length ea of a thin planar convex
lens having a radio a curvaıe of SO mm and an index a
a in NE ase = 100 mm TF a oc AT
laced ar distances 600mm. 200 un. 15 mm. 10 rm. an
ines postive uni = Yams near refer
‘You cn qual check hist witha Simple mes ens
oF onto a white shes of paper.
sien onthe ot and heron poss = fk and,
Ta he eco SHY ies
ers > 2 and Ry < 0.00 tha th et hand ies pa
ine Adding Ey (31d 5. neh
a 14) nd
ren am co hs tem hei
ave the very useful Thin-Lems Equation, often refered tu
1,1 La x
se wt i y= Te pois V a Ve
eo se
Je compat the foc Length ea of a thin planar convex
lens having a radio a curvaıe of SO mm and an index a
a in NE ase = 100 mm TF a oc AT
laced ar distances 600mm. 200 un. 15 mm. 10 rm. an
ines postive uni = Yams near refer
‘You cn qual check hist witha Simple mes ens
oF onto a white shes of paper.
ac Tat image distance approximates f-Now move the
ir ies. As lea image af he mp an be
Frere was be abl where the fates al intrest the
the images it
Focal Points and Planes
gure 15 summarize peor some oe tuto
Imre sw
Th foal en in (a and (6) o Fi, 515 are eq, es
nei low han, > tn oth cases > Dand A; 0
(band eal image a) fre, = ad coreguendy y
ispegaive-loy ae)
but Dy wheres
ce tha ach insane te pricy convenient
a ar thigh he eater of he Tes wih, esse is
Demendicularto-both surfaces, is undevat Suppose,
parle 1 ts incidenr direction, asi Fig 516. We maintain
‘optical center D of he lens. To see thi, dran cv parle
planes: ne om each ie tanent to he lens any pi of
be shown hat he paral ay traversing AB ener and ees
and BOC, ae similar, in the geomeirie
sense, and therefore thse sides are proportional Hence
locaton uf Os constant. independent oA and B.A we saw
eier Probe 230 and Fig P34) aay Inca med.
Figure 5.15 Focas tr come
ir ies. As lea image af he mp an be
Frere was be abl where the fates al intrest the
the images it
Focal Points and Planes
gure 15 summarize peor some oe tuto
Imre sw
Th foal en in (a and (6) o Fi, 515 are eq, es
nei low han, > tn oth cases > Dand A; 0
(band eal image a) fre, = ad coreguendy y
ispegaive-loy ae)
but Dy wheres
ce tha ach insane te pricy convenient
a ar thigh he eater of he Tes wih, esse is
Demendicularto-both surfaces, is undevat Suppose,
parle 1 ts incidenr direction, asi Fig 516. We maintain
‘optical center D of he lens. To see thi, dran cv parle
planes: ne om each ie tanent to he lens any pi of
be shown hat he paral ay traversing AB ener and ees
and BOC, ae similar, in the geomeirie
sense, and therefore thse sides are proportional Hence
locaton uf Os constant. independent oA and B.A we saw
eier Probe 230 and Fig P34) aay Inca med.
Figure 5.15 Focas tr come
160 Chapter 5 Gros Oo:
re 515 a os cat oars. a
im bounded parle planes vi espace eat hu
tro anta evito. Tis displasement I propor
Role ee wh or hi lei ese Raye
passing through O may. accordingly, be drawn as weight
pe O midway between the venis “
perl rating ste comes oa fac pa on e
pil ais dig SD, As shown it Fü. 5.17. this ini
Mac ea sch Bundle tering ha narow some wit
Tocusnd ua epheial segment slo centered om Th
undevite aye nora U surface, and therefore passing
be mamo: o can satay be represented as a plane nr
ma 0 the symmetry a and passing though the
Focas tis Known a fca plane Ta he sme way ing
Ali handles rays" onto 4 surf called the second or back
focal plang, cin ig 3.18 Here each pots ste
the endeved ray thous O. Sesto, me Fest nr from
Finite imagery
point our, Ni fet del withthe facta ret many
5.2) Poche mount, imagine the abst ta be sent of
spe celeron Ci Fig SI o, law the
re 515 a os cat oars. a
im bounded parle planes vi espace eat hu
tro anta evito. Tis displasement I propor
Role ee wh or hi lei ese Raye
passing through O may. accordingly, be drawn as weight
pe O midway between the venis “
perl rating ste comes oa fac pa on e
pil ais dig SD, As shown it Fü. 5.17. this ini
Mac ea sch Bundle tering ha narow some wit
Tocusnd ua epheial segment slo centered om Th
undevite aye nora U surface, and therefore passing
be mamo: o can satay be represented as a plane nr
ma 0 the symmetry a and passing though the
Focas tis Known a fca plane Ta he sme way ing
Ali handles rays" onto 4 surf called the second or back
focal plang, cin ig 3.18 Here each pots ste
the endeved ray thous O. Sesto, me Fest nr from
Finite imagery
point our, Ni fet del withthe facta ret many
5.2) Poche mount, imagine the abst ta be sent of
spe celeron Ci Fig SI o, law the
=
5 Be i
Spherical interface, point S wil have a vial image 7
‘atid therefore nel of. With lamer away i
SO née case. each pl on, has a conagie polo on
‘rani! theory. these surfaces van be considered planar ths
‘rl pana jst normal othe optica! ai il staged
ao sal lavar pon ao amt at ani, Note af
‘vm wil Become cllimated ie parle) and he image
fs wil le on th foal plane (Fg 318)
‘in Fig 519, we can construct a in lens, Once again the
vil generate a final image, Suppose tho that o, in Fig 3.194
spate raie We aliady Krom wha wil happen — he
Siuation is idenicl to Fig 8.196 with the ay decor
ese he find image ford a ens of sal plana
be alla
ct norm tothe optic asl
len can be determine, particularly simp, wih ray di
ms To nd the image othe object in Fig 520 ne mu
sa
fer tat pt Ban potion to
points, there are thee rvs thar ate especially o) o app
lens O. The oer two ray? und ray-d make u ofthe fact
shea y posing rouge fol point vil emerge fom the
um when sketching u daran, draw the en diameter
‘the vertical exten roughly he ive of he foal cat Then
Toc ge ui ya yor he
Fee 520. asa ew yr ean a
5 Be i
Spherical interface, point S wil have a vial image 7
‘atid therefore nel of. With lamer away i
SO née case. each pl on, has a conagie polo on
‘rani! theory. these surfaces van be considered planar ths
‘rl pana jst normal othe optica! ai il staged
ao sal lavar pon ao amt at ani, Note af
‘vm wil Become cllimated ie parle) and he image
fs wil le on th foal plane (Fg 318)
‘in Fig 519, we can construct a in lens, Once again the
vil generate a final image, Suppose tho that o, in Fig 3.194
spate raie We aliady Krom wha wil happen — he
Siuation is idenicl to Fig 8.196 with the ay decor
ese he find image ford a ens of sal plana
be alla
ct norm tothe optic asl
len can be determine, particularly simp, wih ray di
ms To nd the image othe object in Fig 520 ne mu
sa
fer tat pt Ban potion to
points, there are thee rvs thar ate especially o) o app
lens O. The oer two ray? und ray-d make u ofthe fact
shea y posing rouge fol point vil emerge fom the
um when sketching u daran, draw the en diameter
‘the vertical exten roughly he ive of he foal cat Then
Toc ge ui ya yor he
Fee 520. asa ew yr ean a
Figure 521 shows how any nf these es rays locale
es back to he work of Rober Smith as long apo a 178
This praia procedure an be made evensimplr by eel:
522) Presumabl.i we were o extend eve incoming ray
Ei beenssaped acorcuming a atone on at plane Ts
ankam to syne that he two principal plane ofa thin
5225, > Ont}, O. Here the Image ait e vete,
eher 13, > Obey, > Ori righteide up 0r erect
‘Omen that wiangles AOF, an PAPE, ate nla Ego
hie i cou, he Gain Lens Equation (5.17
Per on
es back to he work of Rober Smith as long apo a 178
This praia procedure an be made evensimplr by eel:
522) Presumabl.i we were o extend eve incoming ray
Ei beenssaped acorcuming a atone on at plane Ts
ankam to syne that he two principal plane ofa thin
5225, > Ont}, O. Here the Image ait e vete,
eher 13, > Obey, > Ori righteide up 0r erect
‘Omen that wiangles AOF, an PAPE, ate nla Ego
hie i cou, he Gain Lens Equation (5.17
Per on
Roue 522
sement of which appeared in Newton's Optik in 1704
The signs Of, and ja reckoned with respect o thi on.
E (523) that x, and 1, have like signs, which means thatthe
dt and image must be om poste sides of thelr respective
cl pois. This a yoo thing forte neophyte orermem
Fern making thee hasty rshand ry diagrams for bic
Beorshe already infamous
The ai ol e tasverse dimensions of the inal image
fame by any otal sytem othe corresponding dimension
‘ihe objets defined ste leer tenses magni
Orio Fa (520)
mi 625)
usa postr My connotes an ere image, while negative
alas means the Image ix inverted (see Table 5.2). Bea in
‘ind thats, and a, are both positive fo real objects and
ings Cet, then, al real images formed bya singe in
lis will be inverted. The Nevionian expression for he zug
fication follows rom Eas (5.19) and (522) ad Fig. 5.22
Me 626.
etc magnification sa bit ofa misnomer, since the mas
52 tes 169
TABLE 52_Meanings Associated withthe Signs
of Various Tin Lens and Spherical Interface
Parameters
Quanity Sin
1 © =
nit of My can certain be les ha 1, in which cave the
image smaller than the objet, We have, = — shen the
happens (Eg. (S.17)Lony whens, = = 2 This ws out
Bet configuration in which de ober and image area close
Problem 5.19). TableS 3 summarizes a number of imape con
Figuras res Tom the jataposion oath en ad à
TABLE 5.3 Images of Real Objects Formed by
Thin Lences
Comer
Gosse
sement of which appeared in Newton's Optik in 1704
The signs Of, and ja reckoned with respect o thi on.
E (523) that x, and 1, have like signs, which means thatthe
dt and image must be om poste sides of thelr respective
cl pois. This a yoo thing forte neophyte orermem
Fern making thee hasty rshand ry diagrams for bic
Beorshe already infamous
The ai ol e tasverse dimensions of the inal image
fame by any otal sytem othe corresponding dimension
‘ihe objets defined ste leer tenses magni
Orio Fa (520)
mi 625)
usa postr My connotes an ere image, while negative
alas means the Image ix inverted (see Table 5.2). Bea in
‘ind thats, and a, are both positive fo real objects and
ings Cet, then, al real images formed bya singe in
lis will be inverted. The Nevionian expression for he zug
fication follows rom Eas (5.19) and (522) ad Fig. 5.22
Me 626.
etc magnification sa bit ofa misnomer, since the mas
52 tes 169
TABLE 52_Meanings Associated withthe Signs
of Various Tin Lens and Spherical Interface
Parameters
Quanity Sin
1 © =
nit of My can certain be les ha 1, in which cave the
image smaller than the objet, We have, = — shen the
happens (Eg. (S.17)Lony whens, = = 2 This ws out
Bet configuration in which de ober and image area close
Problem 5.19). TableS 3 summarizes a number of imape con
Figuras res Tom the jataposion oath en ad à
TABLE 5.3 Images of Real Objects Formed by
Thin Lences
Comer
Gosse
We ate nan pono ENE hee TaN
Estuviotol sine cents cone lens To th end, op
peta a dist point source sends out cone of hate
meres y poe Tene PH 525) 1 Whe sour At
iy, so far aay ia igh jn as wel be ily
‘hag. 5.2% ad wil e brought topeher th ol pi
away, Become fra ntm the ens ron, and the ays
the aya do no diverge greatly the le ends cach one int
Aa the nyse diverging o song thatthe lens can.
Tenge bring bem nto convergence and dry emerge parallel
rayo enge so much on emtring the ens that they sl
orge sing. The image pont io Merl tier
Figer 521 late the behavior: pti Ar the
object approaches the lens.
roan Wh Ue objec Vn Ta away age sa,
inver, rd mined M,< sus ee fhe fea
plane As the objet aperache he ns the Image il el
ever und mig M, < 1) moves anay rom ie fo
plane to the ih, ge larger and larger Wit the oc
and excl bth of which qui a muii. el image. By
inverted is now life size tha is, My = L This the usual
tote ich and continues 1 increase in size. This configura
compete fre
mags ting sere im sp pu im opie down
Wen the object asses a distance fom the lens of pre
y oe ocal lene image his eet ove lt
est clover than one focal length, the age
Estuviotol sine cents cone lens To th end, op
peta a dist point source sends out cone of hate
meres y poe Tene PH 525) 1 Whe sour At
iy, so far aay ia igh jn as wel be ily
‘hag. 5.2% ad wil e brought topeher th ol pi
away, Become fra ntm the ens ron, and the ays
the aya do no diverge greatly the le ends cach one int
Aa the nyse diverging o song thatthe lens can.
Tenge bring bem nto convergence and dry emerge parallel
rayo enge so much on emtring the ens that they sl
orge sing. The image pont io Merl tier
Figer 521 late the behavior: pti Ar the
object approaches the lens.
roan Wh Ue objec Vn Ta away age sa,
inver, rd mined M,< sus ee fhe fea
plane As the objet aperache he ns the Image il el
ever und mig M, < 1) moves anay rom ie fo
plane to the ih, ge larger and larger Wit the oc
and excl bth of which qui a muii. el image. By
inverted is now life size tha is, My = L This the usual
tote ich and continues 1 increase in size. This configura
compete fre
mags ting sere im sp pu im opie down
Wen the object asses a distance fom the lens of pre
y oe ocal lene image his eet ove lt
est clover than one focal length, the age
PRE
2 1
ss
=
FE RS
CSS
vues
iu ght sd up. and enlarged,
"e configuration of De moss gie.
ta me central se he hgh of the real ase Fi
525), Became tht ry diverges rom he en xi. e ie
of he image inrenses rapidly a he objet approaches F
Nat, to that the anormaton from oa image space
sat inc al ofthe objet space fom 2/00 init
eof the en, a compre in Ihe age space Been
Fad fon height teens Fur 525 sages ht
image space «dtd nth sem that advance pjs
arm ward te ens ha the fest of hanging be ge
‘spdingsaccesiv changes ithe beg fhe image. Tis
relative “anemia” of distanicobc space scaly obser
be using telesope te, ong focal len les) Youve
probably sea the efect In motion peu sho ous a
us a grat tance Lowar he camen, Bu Pay
1510 make progress Dec Ne perceived Aue
irerenses very MU despite a efor.
Freamany. abe sage the dimension otc a
nel copy thee dimensional ion of ace Te opts!
‘ina dimension ofthe image Te lomtudinal magni
"Han. Me which eines 1 the aa ection, ls defined as
isis the aio of aninfinkesimal xia engi in the region of
the image o he covesponsing length ne region of he
Mia Mi 62
‘shih implies ar a postive di, eorespnd oa gave
stad vice versa In cher woes finger pointing toward e
Form the image ofa window on a see of paper, using a
simple convex les. Assuming a lovely arre! sen, age
he dista mes on the sre Now moe the pape um.
‘he les, o ati mesi a diferent region of ve nage
Thin-Lons Combinations
‘Our use eres noto scone point isthe init
oder es design, at rather gaia the amily neces
sommes
2 1
ss
=
FE RS
CSS
vues
iu ght sd up. and enlarged,
"e configuration of De moss gie.
ta me central se he hgh of the real ase Fi
525), Became tht ry diverges rom he en xi. e ie
of he image inrenses rapidly a he objet approaches F
Nat, to that the anormaton from oa image space
sat inc al ofthe objet space fom 2/00 init
eof the en, a compre in Ihe age space Been
Fad fon height teens Fur 525 sages ht
image space «dtd nth sem that advance pjs
arm ward te ens ha the fest of hanging be ge
‘spdingsaccesiv changes ithe beg fhe image. Tis
relative “anemia” of distanicobc space scaly obser
be using telesope te, ong focal len les) Youve
probably sea the efect In motion peu sho ous a
us a grat tance Lowar he camen, Bu Pay
1510 make progress Dec Ne perceived Aue
irerenses very MU despite a efor.
Freamany. abe sage the dimension otc a
nel copy thee dimensional ion of ace Te opts!
‘ina dimension ofthe image Te lomtudinal magni
"Han. Me which eines 1 the aa ection, ls defined as
isis the aio of aninfinkesimal xia engi in the region of
the image o he covesponsing length ne region of he
Mia Mi 62
‘shih implies ar a postive di, eorespnd oa gave
stad vice versa In cher woes finger pointing toward e
Form the image ofa window on a see of paper, using a
simple convex les. Assuming a lovely arre! sen, age
he dista mes on the sre Now moe the pape um.
‘he les, o ati mesi a diferent region of ve nage
Thin-Lons Combinations
‘Our use eres noto scone point isthe init
oder es design, at rather gaia the amily neces
sommes
SK =
NL
apprit allons Reinemenis reihen added che
einer gos om to the prodigious and more enact ay tin
computers Evens, the Simple thinens concep provides a
highly inal hai fr preliminary calculations In a rond
range of arn
No es fatally lin the wit seme of having a
{hin lens (ke. one that i thin in comparison to its diameter),
Almont al spectacle lese, which, by he way, have been
sd ar est since Me incl century) a= in is category
‘When ther of corvatre ar ape and the les ameter is
{is sor would generally have large focal length, compar
=b Fae 529-1
in thickness would be quite eal
telescope objectives it at description perfects
vin Jens combinations. The approach wil be fil si
ple kan te more elabora Waal tesiment or ho
each o pare the mater io te neXt chee
Coir two thin positive lenses L and L separated by à
distanced whichis sale thin th focal length, a Pi
5.28, The vesalting image can be located graphically asf
low. Overlooking Ly for moment, conos the image
pace cough the lens object and image fos. Fa and F,
respective. The object iin a normal plane, o tal tuo ay
‘termine the tp ofthe image. und perpendicular o he opt
‘lati Hide ns orto, Ray hen one running.
NL
apprit allons Reinemenis reihen added che
einer gos om to the prodigious and more enact ay tin
computers Evens, the Simple thinens concep provides a
highly inal hai fr preliminary calculations In a rond
range of arn
No es fatally lin the wit seme of having a
{hin lens (ke. one that i thin in comparison to its diameter),
Almont al spectacle lese, which, by he way, have been
sd ar est since Me incl century) a= in is category
‘When ther of corvatre ar ape and the les ameter is
{is sor would generally have large focal length, compar
=b Fae 529-1
in thickness would be quite eal
telescope objectives it at description perfects
vin Jens combinations. The approach wil be fil si
ple kan te more elabora Waal tesiment or ho
each o pare the mater io te neXt chee
Coir two thin positive lenses L and L separated by à
distanced whichis sale thin th focal length, a Pi
5.28, The vesalting image can be located graphically asf
low. Overlooking Ly for moment, conos the image
pace cough the lens object and image fos. Fa and F,
respective. The object iin a normal plane, o tal tuo ay
‘termine the tp ofthe image. und perpendicular o he opt
‘lati Hide ns orto, Ray hen one running.
tr
== === a
E Pare 528. Im
uber y esti rg De mag focas, a
para me ara. ined. an vend hen he 275 y
Lemay a comergete 6:01 ordiergeno (fe gr aa En
M Fan yuh potion us ema ag
{moto a Se Tieimenecionotnys and she
«sas well : : mer instance the rays approaching L, are diverging from Pi,
“This is pose, andthe intermediate image isto he ight of
== === a
E Pare 528. Im
uber y esti rg De mag focas, a
para me ara. ined. an vend hen he 275 y
Lemay a comergete 6:01 ordiergeno (fe gr aa En
M Fan yuh potion us ema ag
{moto a Se Tieimenecionotnys and she
«sas well : : mer instance the rays approaching L, are diverging from Pi,
“This is pose, andthe intermediate image isto he ight of
TRUE =
‘ero hin lenses I wl ofen be convenient to have a single
String fray, rom £.52,
PRENONS 39,
Mer, and athe abject and image distances espe
‘he mage distance asaisted with an object placed $00 cm
{rom the ist of two positive lenses, Thess intr ar ep
by 20.0 can and have focal lengths of 3. cm and 50.0,
respectively By dc han
SOLO) = SUSO ae
2 30)
and the image sal Haha "mages" it
‘mediate image formed by Ly, he a tramas magic
Sim of the compound lens ls the product ofthe indivi
magnifico. ati,
islet as Problem 5.35 10 stow tht
= apne un
dj a we shod have esd from Fig 2H. image
"The distance fro the lat arase oF an oa system o
‘ack focal enh, eb. Silay the distance roa be
{roa oca length EI Consequently. I weletsa >
approches which combined wth Eg (S31 tells rat,
Sd fy, Hence ram, (329)
Battie special vale of,
‘ero hin lenses I wl ofen be convenient to have a single
String fray, rom £.52,
PRENONS 39,
Mer, and athe abject and image distances espe
‘he mage distance asaisted with an object placed $00 cm
{rom the ist of two positive lenses, Thess intr ar ep
by 20.0 can and have focal lengths of 3. cm and 50.0,
respectively By dc han
SOLO) = SUSO ae
2 30)
and the image sal Haha "mages" it
‘mediate image formed by Ly, he a tramas magic
Sim of the compound lens ls the product ofthe indivi
magnifico. ati,
islet as Problem 5.35 10 stow tht
= apne un
dj a we shod have esd from Fig 2H. image
"The distance fro the lat arase oF an oa system o
‘ack focal enh, eb. Silay the distance roa be
{roa oca length EI Consequently. I weletsa >
approches which combined wth Eg (S31 tells rat,
Sd fy, Hence ram, (329)
Battie special vale of,
and Ef for he indes system in Fig. Sa, where À
cmand f, = +20em. Then
2110 = 30), soy
MT pm ES Tea
tod sinialy £4. = 1S em. Incidentally, notice thai
f+ f plane waves entering the ompoun lens fom cier
Onserve thar if f=» that, eleves are ought in
bh
¿e sm
“Trea hin ens hasan een focal en fs hat
Two tn aan septa dance geste Bante sn lr sen. De
“This pis hai Were ae N ch less in SOREL
isd i en
Ph ik
Many ofthese conclusions can he ved a eas gal
Ea o spies Fre SA my tc
530 require a it more ar, Fis, determin the oa login
of the two Jess y imaging a distant source. Then had ore
of the lenses Le) at fied distance slighty reer hai
Jocal length irom te plane of observation re a pce 0
‘nile paper Now comes (he manner at requires Same
Got you don't have an optical bench. Move the second
leas) toward the source, Keeping it reasonably center,
out ay atempts 0 lock ought entering cet
you wil probably sex ured image of your hind ding
Position the Temes So Mat te region onthe seren come
Li Ge. Ms image within the image) Wl become clear and
erect ain Fig 530,
cmand f, = +20em. Then
2110 = 30), soy
MT pm ES Tea
tod sinialy £4. = 1S em. Incidentally, notice thai
f+ f plane waves entering the ompoun lens fom cier
Onserve thar if f=» that, eleves are ought in
bh
¿e sm
“Trea hin ens hasan een focal en fs hat
Two tn aan septa dance geste Bante sn lr sen. De
“This pis hai Were ae N ch less in SOREL
isd i en
Ph ik
Many ofthese conclusions can he ved a eas gal
Ea o spies Fre SA my tc
530 require a it more ar, Fis, determin the oa login
of the two Jess y imaging a distant source. Then had ore
of the lenses Le) at fied distance slighty reer hai
Jocal length irom te plane of observation re a pce 0
‘nile paper Now comes (he manner at requires Same
Got you don't have an optical bench. Move the second
leas) toward the source, Keeping it reasonably center,
out ay atempts 0 lock ought entering cet
you wil probably sex ured image of your hind ding
Position the Temes So Mat te region onthe seren come
Li Ge. Ms image within the image) Wl become clear and
erect ain Fig 530,
170. Crapo 5. sooner
Figure SL oA postive nd sar ns comprate, eta
(QED and the Lens
apt fr Feat Principle that Keeps us thinking in
forms of optical pato omg und at naar Tes to
Feynman treatment of Quantum Elecuodyamics. Keen ın
‘ore tha the conceptual machines for calculaig dhe ess
SS obueratios. Ad oo mat how sophisticated a theory i
ica be inten wäh even the ost ordinary
(QED worldview, um 10 Fig. 4.68 andthe mir for
Light goes fom: point St the mir
semendows number f posible
tins. In QED, ech path has an associated pronabiily amp
to point Patong a
tke hich has a phase angle proportional othe teaver
eons rows the pus mediately adjacent 1 e one that hs
te minimum OPL
si apprit things by diving he ma
CINE reer of seperti poss Nah par und
ere ati robot ampliado: corespondi seh
ome: Of coun there should tot more tar plo 5
a ite prohabiiy-ompliads phsor sccited with
ete a pren lotes blo of
pa u >
Freie 32 FE ws ED Aa
Figure SL oA postive nd sar ns comprate, eta
(QED and the Lens
apt fr Feat Principle that Keeps us thinking in
forms of optical pato omg und at naar Tes to
Feynman treatment of Quantum Elecuodyamics. Keen ın
‘ore tha the conceptual machines for calculaig dhe ess
SS obueratios. Ad oo mat how sophisticated a theory i
ica be inten wäh even the ost ordinary
(QED worldview, um 10 Fig. 4.68 andthe mir for
Light goes fom: point St the mir
semendows number f posible
tins. In QED, ech path has an associated pronabiily amp
to point Patong a
tke hich has a phase angle proportional othe teaver
eons rows the pus mediately adjacent 1 e one that hs
te minimum OPL
si apprit things by diving he ma
CINE reer of seperti poss Nah par und
ere ati robot ampliado: corespondi seh
ome: Of coun there should tot more tar plo 5
a ite prohabiiy-ompliads phsor sccited with
ete a pren lotes blo of
pa u >
Freie 32 FE ws ED Aa
a pa al the phasor (each assed o Bethe sate size
ds ik of photos arriving at Putin the phasors
‘Sure ic very high probably o ight reaching via
de ens. In the langage of QED. a fens focuses tight by
aug alle content probably amples have the
same phase angle
heal ni the pss angles wilder proportion
eso place ip tol wl rally Sica, ande
probably amplitud wil nay diminish quickly ot wot
$beomtnuusly so. Notice that he probably dirons
ista single infinitesimally narrow pie; the ight canot he
ec td to ero what hapem, happens rally aná con
anh iKnow a e Ay pate 13
5.3 Stops ===
53.1 Aperture and Field Stops
Th ininseal finite nature oF al les demande at hey
ait aly a fraction ofthe encegy ented by a point source
Th physical limitation presents hy the pipers of imp
joan image. In that respec. e robert or clar dan
nes Any element, be ie the im of a lo or a separate
‘Bop, tat determine tbe amount flight rechng the
ps Koa a Ih aperture tap abies AS) The
sable Tapie this usally Tocted behind he
aperure stop. Evidemiy, 3. determine, the lighegsthering
obit ofthe en x a whole Ax shown in Fig 833.
oblique ray can sil enters system f is sr. Use
ey ofthe image. Te clement iting sive or angular
llth eld stop or SK etemines he eda view of
33 sus im
A inrument. ina eames the edge ati i Roue
The image plan and serves ste fed sop. Tas, wie th
reaching the conjugate image pin (Pg. 9.3). te ed
region above the top nor he region below the Dam ofthe
‘object im ig. 5.38 pase he eld sip, Opening the Cru
pere top would sus the system o acoplar nen
Point In comas, opening the field stop woul allow the
regions beyond the temáis of the obje wich were pe
iba Blocked 0 be image
5.3.2 Entrance and Exit Pupils.
ots once Tun delerming whether oF no ven
Simpy an ae of he pertare stop Th entrance pup of
system is he image othe aperture lp as sen rom an ax
point on the object through Bose elements preceding the
Sta. here aren Tenses eee obje nthe AS the
ler self server as Me entrance ppl. To lue the pit.
examine Fig 5.38, which va lene witha rear aperture op.
and magnified. It canbe located by sending a few rays out
forth edges oF the AS. the al way. In cota the
ds ik of photos arriving at Putin the phasors
‘Sure ic very high probably o ight reaching via
de ens. In the langage of QED. a fens focuses tight by
aug alle content probably amples have the
same phase angle
heal ni the pss angles wilder proportion
eso place ip tol wl rally Sica, ande
probably amplitud wil nay diminish quickly ot wot
$beomtnuusly so. Notice that he probably dirons
ista single infinitesimally narrow pie; the ight canot he
ec td to ero what hapem, happens rally aná con
anh iKnow a e Ay pate 13
5.3 Stops ===
53.1 Aperture and Field Stops
Th ininseal finite nature oF al les demande at hey
ait aly a fraction ofthe encegy ented by a point source
Th physical limitation presents hy the pipers of imp
joan image. In that respec. e robert or clar dan
nes Any element, be ie the im of a lo or a separate
‘Bop, tat determine tbe amount flight rechng the
ps Koa a Ih aperture tap abies AS) The
sable Tapie this usally Tocted behind he
aperure stop. Evidemiy, 3. determine, the lighegsthering
obit ofthe en x a whole Ax shown in Fig 833.
oblique ray can sil enters system f is sr. Use
ey ofthe image. Te clement iting sive or angular
llth eld stop or SK etemines he eda view of
33 sus im
A inrument. ina eames the edge ati i Roue
The image plan and serves ste fed sop. Tas, wie th
reaching the conjugate image pin (Pg. 9.3). te ed
region above the top nor he region below the Dam ofthe
‘object im ig. 5.38 pase he eld sip, Opening the Cru
pere top would sus the system o acoplar nen
Point In comas, opening the field stop woul allow the
regions beyond the temáis of the obje wich were pe
iba Blocked 0 be image
5.3.2 Entrance and Exit Pupils.
ots once Tun delerming whether oF no ven
Simpy an ae of he pertare stop Th entrance pup of
system is he image othe aperture lp as sen rom an ax
point on the object through Bose elements preceding the
Sta. here aren Tenses eee obje nthe AS the
ler self server as Me entrance ppl. To lue the pit.
examine Fig 5.38, which va lene witha rear aperture op.
and magnified. It canbe located by sending a few rays out
forth edges oF the AS. the al way. In cota the
sit puis the image the A. a seen from an il point
on the image plane trough the nerpse Tenses there
cs ta he ono igh sly emerge opti
ten fs determined by te ene pupil. we
Few 535 on etre so.
RH coated by the exit pop No ays om
Ub image pane
"o ws atelesope ora monocular as camera lens, a
sit nach an exemal fon aperture sop 10 Sono De
represents à similar amangement in which the entrance mé
st pup ation shouldbe sel evident The a two
aus ici à ray labeled he ee a IL defied tO
center of the apertre stop. The chief ra enters he opti
ma pap rad eaves the sem along hte pas
sed wit cankal bundle ol sf pont on he Oj
ech behves st conta ofthe Bunde and ie
igure 5.36 depicts a somewhat more involved aang
nem: The two ray shown ae those that are sal te
he pri) a he objet hat oe accorded by I
Te ail object pon hemor marin othe tance pop
‘aca aperture stop each component ofthe stem must be
«nro pupil Te element hase image o comence un
en the aperture stp ofthe syle or tha objet pi
Probl $4 ese wi aw thc Kind of Cll.
image plane becomes natower asthe object point mavesaff
A The elective aperture op. which fr he il ale
‘ays asthe im fas een makes roused forthe of
2 ble. The ress a pada fading ou ofthe nage a
ons Fea ts periphery. a process Knows as vignetting
“Te actions and size ofthe papi of an apical pe
ap I ppl the ee ee il ay om 2 mm
nm, depending onthe genoa ucinaton level Tse
on the image plane trough the nerpse Tenses there
cs ta he ono igh sly emerge opti
ten fs determined by te ene pupil. we
Few 535 on etre so.
RH coated by the exit pop No ays om
Ub image pane
"o ws atelesope ora monocular as camera lens, a
sit nach an exemal fon aperture sop 10 Sono De
represents à similar amangement in which the entrance mé
st pup ation shouldbe sel evident The a two
aus ici à ray labeled he ee a IL defied tO
center of the apertre stop. The chief ra enters he opti
ma pap rad eaves the sem along hte pas
sed wit cankal bundle ol sf pont on he Oj
ech behves st conta ofthe Bunde and ie
igure 5.36 depicts a somewhat more involved aang
nem: The two ray shown ae those that are sal te
he pri) a he objet hat oe accorded by I
Te ail object pon hemor marin othe tance pop
‘aca aperture stop each component ofthe stem must be
«nro pupil Te element hase image o comence un
en the aperture stp ofthe syle or tha objet pi
Probl $4 ese wi aw thc Kind of Cll.
image plane becomes natower asthe object point mavesaff
A The elective aperture op. which fr he il ale
‘ays asthe im fas een makes roused forthe of
2 ble. The ress a pada fading ou ofthe nage a
ons Fea ts periphery. a process Knows as vignetting
“Te actions and size ofthe papi of an apical pe
ap I ppl the ee ee il ay om 2 mm
nm, depending onthe genoa ucinaton level Tse
Figure 8.36 ot an ste
eat the term nigh lasves—they were quite popular on the instrument Obviously. telescopic sigh for hise pow
(oc during the Second World War I cotes. adaylight ered il should havea lage exit pupil locates for enough
cre ent pul te easier it ain your eve propery ih 7
Ree 837 vesting
aS,
eat the term nigh lasves—they were quite popular on the instrument Obviously. telescopic sigh for hise pow
(oc during the Second World War I cotes. adaylight ered il should havea lage exit pupil locates for enough
cre ent pul te easier it ain your eve propery ih 7
Ree 837 vesting
aS,
174 apar 5 Gaceta ces
5.3.3 Relative Aperture and f-Number
Suppose we cllect the ight for an extended source and
form an image of sig a lens (or mirror). The amos o
sere athe By the Teas (Or minor) from some smal
‘efion of dista souse wil be direct proportional o the
ars of eas or. more general 1 the area ofthe entrance
rave Obviously, the somos wee aer with very arrow
‘am, tis would mat necesa be re ve regles ons
y wil be spread aros comesponding ion ofthe image
{Tig 5.38 The energy pr unt arca pr nit ie ti. he lux
density radiance) wil be inversely proponional to the
“The eme pup ze. tl, vanes there of
diameter D. Furthermore the image arca will vary as the
‘quar ft lateral dimension, which in ur [Egs (52 and
(261 proportional 2%. (Keepin min Ut we ar lit
thou an extended object cater than a point source. Ene at
ter case the image woul be confine 1 à very mill area
independent ol /) Ths the ux density a he image pane
saris a (D/7?. The ratio ic Know athe relaie ape
tur anditsinvencis the focal rai sombrero
where f/# should be understood asa single symbol. For
length hs anf number of 2 hc usually designated 2
Faure 5.3 lasts the point by showing a chim lens behind
‘arable is iaphragm operating at cer 72007. A
smaller umber clearly permite moe light o reach the
image plane.
Camera lenses ar usally specifies by hele focal lengths
and tres pow acne or ample, yor mit ce "30
mm FA onthe hare of a lene Since te plotorapt
Espovar tate proponional othe square ofthe umber
the tris sometimes spoken of a the speed ofthe les. An
f/1A tes i ai 0 ve twice fast ae an f/2 lens, Dali
lens diaphragn have number eekings of L 14.2. 2.8.4
SGA. 11, 16,2, and soon. The largest eave apr in
‘move peal. Fach coneccuive diaphragm sing increases
Ihe number by a alipieaive factor of V2 (numerically
200008
5.3.3 Relative Aperture and f-Number
Suppose we cllect the ight for an extended source and
form an image of sig a lens (or mirror). The amos o
sere athe By the Teas (Or minor) from some smal
‘efion of dista souse wil be direct proportional o the
ars of eas or. more general 1 the area ofthe entrance
rave Obviously, the somos wee aer with very arrow
‘am, tis would mat necesa be re ve regles ons
y wil be spread aros comesponding ion ofthe image
{Tig 5.38 The energy pr unt arca pr nit ie ti. he lux
density radiance) wil be inversely proponional to the
“The eme pup ze. tl, vanes there of
diameter D. Furthermore the image arca will vary as the
‘quar ft lateral dimension, which in ur [Egs (52 and
(261 proportional 2%. (Keepin min Ut we ar lit
thou an extended object cater than a point source. Ene at
ter case the image woul be confine 1 à very mill area
independent ol /) Ths the ux density a he image pane
saris a (D/7?. The ratio ic Know athe relaie ape
tur anditsinvencis the focal rai sombrero
where f/# should be understood asa single symbol. For
length hs anf number of 2 hc usually designated 2
Faure 5.3 lasts the point by showing a chim lens behind
‘arable is iaphragm operating at cer 72007. A
smaller umber clearly permite moe light o reach the
image plane.
Camera lenses ar usally specifies by hele focal lengths
and tres pow acne or ample, yor mit ce "30
mm FA onthe hare of a lene Since te plotorapt
Espovar tate proponional othe square ofthe umber
the tris sometimes spoken of a the speed ofthe les. An
f/1A tes i ai 0 ve twice fast ae an f/2 lens, Dali
lens diaphragn have number eekings of L 14.2. 2.8.4
SGA. 11, 16,2, and soon. The largest eave apr in
‘move peal. Fach coneccuive diaphragm sing increases
Ihe number by a alipieaive factor of V2 (numerically
200008
re Mc dens hy one BTR the ee art
SOM second, 721/250 af send. or
<a oember of 189. The entrance pupi and oca rh of
aresope, mia prime focal eng 01.66 inches, san
5.4 Mirrors
Xray. wliaviolet, and infrared reg
Be same cum si refais Por ear =
Sunpleely opaque inthe visible (se photo on p. 73). As we
‘mor mich simply be ise of bik gs or fly
sates have bec he cepted Sanda For quality mi
pleno (ein laser) bere con bic vl les due
‘Ont sures canna be oler, minor ord of mul
seed detec ms (ce Section 9.9 are indipensahe
De ecology nb no
54.1 Planar Mirrors
ior Sofia. hos lane lanar
ehckesurtced The lar type ae mos om
SOM second, 721/250 af send. or
<a oember of 189. The entrance pupi and oca rh of
aresope, mia prime focal eng 01.66 inches, san
5.4 Mirrors
Xray. wliaviolet, and infrared reg
Be same cum si refais Por ear =
Sunpleely opaque inthe visible (se photo on p. 73). As we
‘mor mich simply be ise of bik gs or fly
sates have bec he cepted Sanda For quality mi
pleno (ein laser) bere con bic vl les due
‘Ont sures canna be oler, minor ord of mul
seed detec ms (ce Section 9.9 are indipensahe
De ecology nb no
54.1 Planar Mirrors
ior Sofia. hos lane lanar
ehckesurtced The lar type ae mos om
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