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DIFFRACTION
Diffraction is the penetration of light wave towards the geometrical shadow region around a sharp obstacle
such as the edge of a slit, sharp aperture etc.
(a) In Fresnel class of diffraction, the source and/or screen are at a finite distance from the aperture. The
wave front is either spherical or cylindrical in shape
(b) In Fraunhoffer class of diffraction, the source and screen are at infinite distance from the diffracting
aperture. The wave front is plane.
Single slit Fraunhoffer diffraction
P
A slit of width ‘a’ is divided into N parallel strips of width x. Each strip acts as a
radiator of Huygens’s wavelets and produces a characteristic wave disturbance at
P, whose position on the screen for a particular arrangement of apparatus can be
described by the angle .

a
If the strips are narrow enough – which we assume – all points on a given strip
have essentially the same optical path length to P, and therefore all the light from the strip will have the same
phase when it arrives at P. The amplitudes E0 of the wave disturbances at P from the various strips may be
taken as equal if  is not too large.
The wave disturbances from adjacent strips have a constant phase difference  between them at P, given by
phase difference path difference

2

2
 

 x sin  

Thus at P, N vectors with the same amplitude E0, the same

frequency and the same phase difference DF between adjacent

members combine to produce a result disturbance. In the
R
limiting case (N → ∞),  → 0
R
From geometry
E
 
E  2R sin   ,   m
R
2
E
 
E  m .sin  

 /2
2
sin 

, where  
Or E  E m .

2
En

Em
As

2

a sin     
 sin  
As I  E  I  I m 

  
In brief
 sin  
E  E m 
;
  
 a sin 

2
2
 sin  
I  I m 
 ;
  
  a sin 

2

2
Single slit diffraction formula
Minima occur when, a = np
n – 1, 2, 3…….
 a sin 
 x   sin   x


n
.
If q is small,  min 
Condition for minima
a
For n  3, it can be assumed that the nth secondary maximum is midway between the adjacent minima.
If we know the shape of front at t = 0 then from Huygens principle allows us to determine the shape of wave
front at any time t. Let us consider a diverging wave originating from point 0. f1 f2 represent a portion of the
spherical wave front at t = 0 Now according to Huygens principle, each point of the wave front is the source
of a secondary disturbance and the wavelets emanating from these points spread out in all dandies with the
speed of the wave. These wavelets emanating from the wave front are usually referred to as secondary
wavelets and if we draw a common tangent to all these spheres we obtain the new position of the wave front
at dater time. Thus if we wish to determine the shape of the wave front at t =  we draw the sphere of radius
v from each point on the spherical wave front. The common tangent draw to all these spheres gives the new
position of the wave front C1 C2 with center at O. we also have a back wave which is shown as 1 2.
According to Huygens the amplitude of the secondary wavelength in forward direction and zero in the
backward direction
Sandeep tiwari