Diffraction

1. Diffraction

2. Diffraction
•When waves encounter obstacles, the
bending of waves around the edges of an
obstacle is called “DIFFRACTION”.

3. DIFFRACTION
S
S
A
B
FIG 1.1

4. Here we have a source s emitting waves having plane
wavefronts.
As the wavefronts pass through the slit ab,they are
diffracted and are able to reach even those regions
behind ab which they would be unable to reach had
the rays not bended.
One more thing to be noted here is that the shape of
the wavefronts change as they pass through the slit.
The reason for this bending can be explained with the
help of huygens principle.

6. Diffraction by single slit,& its
pattern.

7. Huygen’s principle:-each particle lying on any
wavefront acts as an independent secondary source and
emits from itself secondary spherical waves.After a very
small time interval, the surface tangential to all these
spherical wavelets,gives the position and shape of the new
wavefront.
It will be more clear from the following example of plane
wavefronts.
Let p1,p2,p3,…pn be points very close to each other and
equidistant from each other on the plane incident wavefront.

8. To obtain the new wavefront we consider p1,p2,..Pn as independent
sources and circular arcs with same radius from each of these points.
Now the plane a’ tangential to all these imaginary surfaces gives the
new wavefront.
We move on to using huygen’s principle for explanation of
diffraction.
Consider figure 1.1
AA’
P1
P2
P3
P4
PN

9. The dimensions of the slit are finite.As a result,applying
huygen’s principle we can say that the new wavefront
obtained will be something like the surface shown in figure.

10. Types of diffraction
There are two types of diffraction.
1)Fresnal diffraction
2)fraunhoffer diffraction

11. Fresnel diffraction
S
Fraunhofer diffraction
S

12. I.FRESNAL DIFFRACTION
When the distance between the slit ab and
source of light s as well as between slit ab
and the screen is finite, the diffraction is
called Fresnal diffraction.
In Fresnal diffraction the waves are either
spherical or cylindrical.

13. I.FRAUNHOFER
DIFFRACTION
If light incident on slit ab is coming from infinite
distance, the distance between obstacle a and
screen c is infinite, the diffraction is called
Fraunhofer diffraction.
In Fraunhofer diffraction the incident waves
should have plane wavefronts.

14. X-Ray Diffraction
•X-rays have wavelengths
comparable to atomic sizes
and spacings, about 10
–10
m
•Crystals and molecules
reflect X-rays in specific
patterns depending on their
structures
X-ray diffraction pattern of myoglobin

15. Interaction of X-Rays with Atoms
•Involves the electrons, primarily

16. Bragg Diffraction

17. Bragg’s Law
lqnd =sin2
•W. H. Bragg and W. L. Bragg, 1913 (Nobel 1915)
•Condition for constructive interference:
•Diffraction from different sets of planes in the
crystal gives a picture of the overall structure

18. Single Slit Diffraction
We have seen how we can get an interference
pattern when there are two slits. We will
also get an interference pattern with a single
slit provided it’s size is approximately l
(neither too small nor too large)
18
Light

19. To understand single slit diffraction, we must consider each
point along the slit (of width a) to be a point source of
light. There will be a path difference between light
leaving the top of the slit and the light leaving the middle.
This path difference will yield an interference pattern.
Path difference of rays to P from top and bottom edge of slit
DL = a sinq  destructive if DL = ml,m=1,2,…
19
Light
P
q
(a/2) sinq
sin = m
a
(m1, 2...) Destructiveq
l
=±±

20. Single Slit
Diffraction
20
Notice that central
maximum is twice as
wide as secondary
maxima
Sinq = m l / W,
Destructive
Dark Fringes on screen
y = L tanq » L (ml/W)
Maxima occur for y= 0
and,
y » L (m±1/2)(l/W)
m=1
m=-1
L