Two coherent point sources S₁ and S₂ vibrating in phase emit light of wavelength λ. The separation between the sources is 2λ. Consider a line passing through S₂ and perpendicular to the line S₁S₂ . What is the smallest distance from S₂  where a minimum of intensity occurs?

Dear Sundeep,

See the diagram given below:

Now we know that if I₁and I₂ are the intensities of the given two coherent sources of light.

then

resultant I = I₁ + I₂ + 2 √(I₁I₂) cos δ

δ = phase difference between the two waves coming from the two sources

tan δ = 2λ/y....................1

and also

cos δ = x/2λ.........................2

 where x is the path difference between the waves and y is the distance along S₂ at which  I is minimum

So phase difference must be odd multiples of π

so δ = (2m+1) π

and δ = x * 2π/ λ

         From 2 and above equation we get cos θ = (2m+1)/4  where θ  is shown in the figure

for first minima

m=0

so cos θ = 1/4

tan θ = √15

and from 1

y = 2λ/√15

is the distance at which we get first minima