Diffraction

1. Diffraction
Diffraction is a phenomenon in which light bends around an obstacle.
Grimaldi in 1665 first observed it.
Fresnel explained the phenomenon on the basis of wave theory of
light. The diffraction is due to the finiteness of the wavefront.
The phenomenon of diffraction was explained by considering the mutual
interference of secondary wavelets originating from the various points of
the wavefront, which are not blocked off by the obstacle.
Types of diffraction:
Fresnel diffraction
Fraunhoffer diffraction

2. Diffraction
Differences between Fresnel and Fraunhoffer diffraction
● Fraunhoffer diffraction Fresnel diffraction
Source of light and the screen are Source of light and the screen are
at very large distance from the at finite distance from the obstacle
obstacle
Incident wavefront is a plane Incident wavefront is a spherical
wavefront. wavefront
Initial phase of the secondary Initial phase of the secondary
wavelets is same at all points in the wavelets is different at different
plane of the diffracting device. points in the plane of the diffracting
device.
Use of converging lens or
telescope is necessary for Visible by eye
observations
Diffracted wavefront is plane.
Diffracted wavefront is spherical
e.g. grating
e.g. zone plate

3. Diffraction
● Fraunhoffer diffraction Intensity distribution in single slit diffraction:
P
A
θ
P 0
B

4. Diffraction
As the wavefront is planar, the energy passing through unit area of the wavefront per
second is constant. The intensity associated with the wavefront is also constant over
the entire slit aperture.
a: Width of the slit AB
P: point of focus of incident wave
P’: point at which secondary waves traveling at angle t are focused.
dz : element of wavefront at co-ordinate (0,z)
ρ : distance from P’ to dz.
r: distance of screen from O

5. Diffraction
The amplitude of the wavefront emitted by the element dz is proportional to
length and inversely proportional to ρ.
At the point P’ it produces an infinitesimal displacement which is a spherical
wave expressed by
adz
dy = sin ( ωt−kρ )
ρ
t ρ
=kdz sin2π ( -
T λ )
The resultant displacement at P’ due to the entire wavefront is
+a/ 2
t ρ
y = k ∫ sin2π
−a/ 2
- dz
T λ ( )

6. Diffraction
from the figure,
ρ2 = x 2 + ( z 0 −z )2
0
and
r 2 = x 2 +z 2
0 0
∴ x 2 = r 2− z 0
2
0
hence
ρ 2 = r 2−z 2 + ( z 0 −z ) 2
0
2 2 2 2
=r −z 0 + z 0 +z −2z 0 z
=r 2 +z 2 −2z0 z
=r 2 1−
[ 2 zz 0
r2
z2
+ 2
r ]

7. Diffraction
for Fraunhoffer diffraction,r >> z and z 2 r 2 is negligible as compared to 1.
2
ρ = r 1− 2
[ 2 zz 0
r2 ]
now
2
4 ( zz 0 ) 2
[ 1−
2 zz 0
r 2 ] = 1−
2 zz 0
r 2
+
r4
as
( zz 0 ) 2
4
<<1
r
it can be neglected

8. Diffraction
Continued....