a) In Young’s double slit experiment, derive the condition for (i) constructive interference and

(ii) Destructive interference at a point on the screen.

(b) A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes in a Young’s double slit experiment on a screen placed 1.4 m away. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide.

a)
Conditions of constructive interference and destructive interference.

Consider two coherent waves travelling in the same direction along a straight line.

Frequency of each wave is given by , 

Amplitude of electric field vectors are a₁ and a₂ rspectively.

Wave equation is represented by, 
 

Intensity of the wave is proportional to the amplitude of the wave.

Thus, Intensity of the resultant wave is given by, 

Constructive interference: For maximum intensity at any point, cos  = +1

So, maximum intensity is, 

Path difference is, 

Constructive interference is obtained when the path difference between the waves is an integral multiple of  

Destructive Interference: For minimum intensity at any point, cos  = -1

Phase difference is given by, 
  
Path difference is, 

In destructive interference, path difference is odd multiple of  .
b)
Given,
 
d = 0.28 mm = 0.28 x 10^-3 m
As, 

If n₁ = n then, n₂ = n+1