Polarization Physics Optics.pptx

Polarization Optics Physics

1. Polarization Reference: Optics (4th Edition)[ Ajoy Ghatak ] Optics  (4th Edition) [Eugene  Hecht] A Textbook of Optics [ Brijlal & Subrahmanyam ]

2. If we have a one end of a string up & down then a transverse wave is generated. Each point of the string executes sinusoidal oscillation in straight light (along x- axis) and the wave, therefore, known as a linearly polarized wave.

3. Light as an electromagnetic wave Light is a transverse electromagnetic wave The vibrating electric vector E and the direction of wave propagation form a plane. Plane of vibration/Polarization

4. U npolarized light. Light in which the planes of vibration are symmetrically distributed about the propagation direction of the wave Linearly polarized light. Electric field vector oscillated in a given constant orientation.

5. Effect of polarizer on natural light P A I o I A I o P

6. P A ? θ E o E= Ey = E o Cos θ I=I o Cos 2 θ I o Malus’s Law

7. Polarization by Reflection [Brewster’s Law] µ = tan i p µ = sin i p / cos i p Snell’s law µ = sin i p / sin r r = 90- i p OR r+ i p =90 Sin r = cos i p

8. Refraction

9. Polarization by Double refraction

10. Arrangement of atoms in a crystal can lead to both a structural asymmetry and an anisotropy in the optical properties. The speed of the E-M wave depends on the refractive index n. Therefore phenomenon of double refraction ( birefringence) occurs Ordinary ray—follows snell’s law (n constant) Extraorinary ray – does not follow snells law (n not fixed)

11. The difference  n = n e – n o is a measure of the birefringence. Optic Axis – A direction along which incident light does not suffer double refraction. All crystals having symmetries that are hexagonal, tetragonal, and trigonal are optically anisotropic and will lead to birefringence. In such crystals, an optic axis exists and about which the atoms are arranged symmetrically. Crystals possessing only one such optic axis are known as uniaxial . [Calcite, tourmaline, and quartz] For calcite  n = 1.486 – 1.658 = -0.172, negative uniaxial , while quartz is Positive. The crystal having two optic axis and both the refracted rays are extraordinary are biaxial. [mica, topaz, aragonite]

12. The Calcite Crystal The Calcite is chemically calcium carbonate CaCO 3. (rhombohedron) Each of six faces of the crystal is a parallelogram of 78.08  and 101.92. Two opposite corners A and B are obtuse and called as blunt corners. n e = 1.486 n o = 1.658

13. Nicol Prism A calcite crystal that is cut, polished, and painted, separates the o -ray and e -ray via TIR (total internal reflection). A thin layer of balsam glues two halves of the crystal. Balsam has an index of refraction, n b , which is between that of the o - and e -rays, i.e., n e (1..486) < n b (1.55) < n o (1.66). Thus, the o -ray experiences TIR at the balsam interface and is absorbed by the layer of black paint on the side. The e-ray refracts normally at the balsam interface an leaves the crystal at the bottom. Therefore, the emitted ray can be used as a fully linearly polarized beam.

14. Double refraction Huygen’s Explanation

15. When the light wave strikes of a doubly refracting crystal, every point of the crystal becomes source of two secondary wavelets; (O) rdinary and (E) xtraordinary . For O – ray velocity is same in all the directions, the wave front is spherical. For E – ray velocity, the wave front is ellipoisdal . For Negative uniaxial crystal the sphere lies inside the ellipsoid, while in Positive crystal ellipsoid lies inside the sphere.

16. Optic Axis Optic Axis Calcite (-ve) Quartz (+ve) E-ray O-ray E-ray O-ray Semi major axis = v e t Semi Minor axis = v o t E-ray O-ray Radius = v o t

17. Optic Axis inclined to the refracting face & in the plane of incidence CASE 1 1.1 Oblique incidence During time t = BC/v, in which disturbance from B to C reaches C, the spherical wave (o) front travelled AG = v o t = v o BC/v = BC/µ o Similarly the distance travelled by extra ordinary (e) wave AH = v e t= v e BC/v = BC/µ e

18. The ordinary spherical wave surface acquires a radius BC/µ o The extra ordinary ellipsoidal wave surface has semi minor axis along the optic axis and semi major axis perpendicular to optic axis BC/µ o = semi minor axis or radius of spherical wave BC/µ E = semi major axis ; Where µ E = minimum refractive index for E-ray at Perpendicular to optic axis. CG (Tangent) represents the position of Ordinary wave front and CH represents the position of Extra ordinary wave front. AG represents the direction of O rays while AH gives the direction of E-ray. Both E and O ray travel in different directions and with different velocities.

19. 1.2 Normal Incidence Dotted line is the optic axis The tangent planes CD and GH are parallel and represent the positions of Ordinary spherical and Extraordinary ellipsoidal wave surfaces. The AO and AE are the O and E ray which travel along different path with different velocities.

20. CASE 2 Optic Axis parallel to the refracting face & in the plane of incidence 2.1 Oblique incidence The AO and AE are the O and E ray which travel along different path with different velocities.

21. 2.2 Normal incidence Although the O and E ray are not separated and they travel along the same direction , yet there is double diffraction. As they travel with different velocities a phase difference is introduced between them This property is utilized in quarter and half wave plate [Important]

22. CASE 3 Optic Axis perpendicular to the refracting surface & in the plane of incidence 3.1 Oblique incidence The AO and AE are the O and E ray which travel along different path with different velocities.

23. 3.2 Normal incidence Both O and E travel with the same velocity

24. CASE 4 Optic Axis parallel to the refracting surface & perpendicular to the plane of incidence 4.1 Oblique incidence The AO and AE are the O and E ray which travel along different path with different velocities.

25. 4.2 Normal incidence Although the O and E ray are not separated and they travel along the same direction , yet there is double diffraction. As they travel with different velocities a phase difference is introduced between them

26. Quarter wave plates A thin plate of birefringent crystal having the optic axis parallel to its refracting faces and its thickness is adjusted such that it introduces a quarter wave ( /4) path difference (OR a phase difference of 90 between the e- and o-rays, propagating through it. Path difference () = (µ o -µ e )t = /4 for –ve calcite Path difference () = (µ e -µ o )t = /4 for +ve Quartz

27. Half wave plates A thin plate of birefringent crystal having the optic axis parallel to its refracting faces and its thickness is adjusted such that it introduces a half wave ( /2) path difference (OR a phase difference of 180 between the e- and o-rays, propagating through it. Path difference () = (µ o -µ e )t = /2 for –ve calcite Path difference () = (µ e -µ o )t = /2 for +ve Quartz

28. Superposition of waves linearly polarized at right angles Production of circularly and elliptically polarized light OR For calcite crystal e-ray travels faster than o - ray Along X-axis (e-ray) x = aSin ( ω t+ φ )----(1) Along Y-axis (o-ray) y = bSin ω t-------(2) y/b = Sin ω t-------(3) e-ray Amplitude-a O-ray A θ Amplitude-b

29. Using eq (1) x/a = sin ω tcos φ + cos ω tsin φ x/a = sin ω tcos φ +(1-sin 2 ω t) 1/2 sin φ Using eq (2) (x/a) = (y/b) cos φ +{1-(y/b) 2 } 1/2 sin φ (x/a) –(y/b) cos φ = {1-(y/b) 2 } 1/2 sin φ [(x/a) –(y/b) cos φ ] 2 = {1-(y/b) 2 }sin 2 φ (x/a) 2 +(y/b) 2 cos 2 φ -(2xy/ ab ) cos φ = sin 2 φ -(y/b) 2 sin 2 φ (x/a) 2 +(y/b) 2 (sin 2 φ +cos 2 φ )-(2xy/ ab ) cos φ = sin 2 φ

30. (x/a) 2 +(y/b) 2 -(2xy/ ab ) cos φ = sin 2 φ This is the general equation of ellipse Case (1) if Φ = 0, 2 π , 4 π , 6 π sin Φ = 0 ; cos Φ = 1

31. (x/a) 2 +(y/b) 2 -(2xy/ ab )= 0 (x/a – y/b) 2 = o OR y=(b/a)x [ Straight line] Plane polarized light General equation becomes b a

32. Case (2) if Φ = π , 3 π , 5 π ,…. sin Φ = 0 ; cos Φ = -1 y= - (b/a)x [ Straight line] Plane polarized light General equation becomes b a

33. (x/a) 2 +(y/b) 2 -(2xy/ ab ) cos φ = sin 2 φ Case (3) if Φ = π /2,3 π /2,5 π /2,7 π /2,9 π /2 sin Φ = 1 ; cos Φ = 0 and a≠b (x/a) 2 +(y/b) 2 = 1 Elliptically polarized light General equation becomes

34. Case 3 ( i ) if Φ = π /2,5 π /2,9 π /2 X= asin ( ω t+ Φ ) = acos ω t Y= bsin ω t If ω t = 0; X=a, y = 0 If ω t = π /2 ; X=0, y = b If ω t =3 π /2 ; X=-a, y = 0 If ω t =5 π /2 ; X=0, y = -b b a Anticlockwise (OR Left) Elliptically polarized light

35. Case 3 (ii) if Φ = 3 π /2,7 π /2,11 π /2..etc X= asin ( ω t+ Φ ) = - acos ω t Y= bsin ω t If ω t = 0; X=0, y =-b If ω t = π /2 ; X=-a, y = 0 b a Clockwise (OR Right) Elliptically polarized light

36. (x/a) 2 +(y/b) 2 -(2xy/ ab ) cos φ = sin 2 φ Case (4) if Φ = π /2,3 π /2,5 π /2,7 π /2,9 π /2 sin Φ = 1 ; cos Φ = 0 AND a=b x 2 +y 2 = a 2 Circularly polarized light General equation becomes

37. Case 4 ( i ) if Φ = π /2,5 π /2,9 π /2 X= asin ( ω t+ Φ ) = acos ω t Y= asin ω t Anticlockwise (OR Left) Circularly polarized light a a

38. Case 4 (ii) if Φ = 3 π /2,7 π /2,11 π /2..etc X= asin ( ω t+ Φ ) = - acos ω t Y= asin ω t a a Clockwise (OR Right) Circularly polarized light

39. e-ray Amplitude-a O-ray A θ Amplitude-b

40. Production of elliptically OR Circularly polarized light Optic Axis θ If θ ≠ 45  Elliptically If θ = 45  Circularly b a QWP

41. Analysis of polarized light Operation Unknown light Analyzer Plane polarized Conclusion I max I max

42. Unknown light Analyzer Operation Elliptically OR Partially polarized light ? I max I min I min I max QWP Analyzer Operation I max I max Elliptically OR Partially polarized light ? Elliptically polarized Conclusion

43. Unknown light QWP Analyzer Rotation of analyzer about its own axis I max I max I min Analyzer Rotation of analyzer about its own axis I max I max I min Unknown light QWP Analyzer Rotation of analyzer about its own axis I max I max I Analyzer Rotation of analyzer about its own axis I I I

44. I max I min I max I min Partially polarized Conclusion

45. Unknown light Analyzer Operation Circularly OR unpolarized light ? I I I I QWP Analyzer Operation I I Circularly OR unpolarized light ? Circularly polarized Conclusion

46. I I I I unpolarized Conclusion

47. 50 With achiral compounds, the light that exits the sample tube remains unchanged. The compound is said to be optically inactive . Optical Activity

48. With chiral compounds, the plane of the polarized light is rotated through an angle . A compound that rotates polarized light is said to be optically active .

49. The ability to rotate the plane of polarization of plane polarized light certain substances is called optical activity. Substances are known as optically active substance Dextro rotatory (D-type) Laevo rotatory (L-type) Specific rotation θ α l; θ α c; θ α lc OR θ = Slc OR S= θ / lc [specific rotation]

50. Facts: Optically Active Biological Substance Natural sugar (sucrose C 12 H 22 O 11 , glucose C 6 H 12 O 6 ) is always d- rotatory , while laboratory-synthesized organic molecules are equal in the number of l- and d- rotatory molecules. Most proteins are l- rotatory . Proteins found in meteorite are equal in the number of l- and drotatory form.

51. Fresnel’s Theory of Optical activity The plane polarized light consists of resultant of circularly polarized vibrations rotating in opposite directions with the same angular velocity.

52. x = 0 y=2asin ω t Consider a plane polarized light is incident normally on a doubly refracting crystal. The vibration in the incident beam are represented by x = acos ω t- acos ω t y= asin ω t+asin ω t x1 x2 y1 y2

53. x 1 = acos ω t; y 1 = asin ω t x 2 = - acos ω t; y 2 = asin ω t Anti Clockwise Circular Polarization Clockwise Circular Polarization These circular components travel through the crystal with different velocities. When they emerge from the crystal, there is a phase difference δ between them. In case of quartz (Right handed crystal), the clock wise component will travel faster.

54. X=x 1 + x 2 Y=y 1 +y 2 x 1 = acos ( ω t+ δ ); y 1 = asin ( ω t+ δ ); x 2 = - acos ( ω t); y 2 = asin ( ω t)

55. X = 2asin( δ /2) sin( ω t+ δ /2)…..(1) Y = 2acos( δ /2)sin( ω t+ δ /2)…(2) Resultant vibrations along X and Y axis have the same phase. Therefore, the resultant vibration is plane polarized and it makes an angle δ /2 with the original direction. Therefore plane of polarization is rotated through an angle δ /2 on passing through the crystal From (1) & (2) Y/X = tan( δ /2) Represents, plane polarized light with vibrations inclined at an angle δ /2 with y-axis

56. =t(µ L -µ R ); δ =(2 π / )t(µ L -µ R ) OR Θ = δ /2 =( π / )(µ L -µ R )t

57. Lorent’s half shade Polarimeter The Lorent’s half shade device consists of a semi circular half wave plate ABC of quartz and a semi circular glass plate ADC. These two plates are cemented along AC The HWP introduces a phase difference of  between O and E-ray. The thickness of glass plate is such that it absorbs same amount of light as the quartz plate.

58. Plane of vibration of plane polarized light incident normally on the half shade and is along PQ. The vibrations emerge from glass plate along PQ, while from Quartz plate a phase difference of  is introduces between them. Due to this phase difference the direction of O components reversed.

59. Application: Specific rotation of sugar solution S= θ / lc OR θ = Slc

60. Bi-Quartz Polarimeter It consists of two semi-circular quartz plates cut perpendicular to the optic axis-one left handed and another right-handed. The thickness of the plates chosen that each plate rotated yellow light by exactly 90 . (thickness – 3.75mm for 5893A). Since light is travelling perpendicular to the optic axis each color undergo optical rotation by different amounts: maximum for violet and minimum for red. This leads to rotatory dispersion.

61. Two semicircular quartz plates rotates yellow light exactly by 90  in opposite direction. The red light is rotated by smallest amount say θ and shortest wave length violet is rotated by maximum angle . All other wavelenghts are rotated between θ and  but yellow by 90 . When transmitting direction of N 2 happens to be parallel to AA’, yellow light being at the right angles, it is not transmitted through analyser N 2 . Red and violet make almost equal angles with the transmitted axis of N 2 so these are transmitted equally from both semicircular plates. Thus both appear grey-violet (GV) colored. This color is called Tint of Passage or Sensitive Tint .

62. If the analyser N 2 is rotated clockwise through a small angle so that its transmission direction become say PP’. Then red is almost parallel in right half and violet is parallel in left-half the two circular plates . As a result, these colors transmit maximum and so right half become red or pink whereas left half becomes violet or blue.

63. If the analyser N 2 is rotated anticlockwise through a small angle so that its transmission direction become say CC’. Then red is parallel to direction of transmission in left half and violet is parallel to direction in right half. The result is opposite to one seen when rotated clockwise. The left-half becomes pink-red and right becomes blue-violet. Thus a small rotation changes the colors contrast in the filed of view. This device is far more sensitive than a half-shade device.

64. Twin Paradox. About Relativity As an object approaches the speed of light, time slows down. (Moving clocks are slow) (Moving rulers are short)

65. Earth Mr. A Mr. B Planet X Mr. A stays on Earth and Mr. B travels 10 light-years at 80% of the speed of light.

66. As Viewed From Earth Without Relativity….. x = v t or t = x / v x is light years traveled v is velocity. t is time. t = 10 LY / 0.8c = 12.5 years each way. There and back makes the trip 12.5 x 2 or 25 years!! (This is time as appeared by A i.e. T)

67. As Viewed From Earth With Relativity Mr. A sees Mr. B’s clock is running slow by… γ = 5/3 !! [ γ = ] Therefore the time as read by B ’s clock (Actual time i.e. T o ) = 25 years ÷ γ 25 ÷ 5/3 = 15 years!! 1 1 - β ²

68. Physical Results of Trip Mr. A on Earth ages 25 years!! Mr. B, traveling at 80% the speed of light ages 15 years!!