Two coherent sources whose intensity ratio is `64 : 1` produce interference fringes. The ratio of intensities of maximum and minima is

Options

A. `9:7`
B. `8 :1`
C. `81 : 49`
D. `81 : 7`

Answer

c

Explanation

The intensity of maxima `I_(max)= (sqrt(I_(1))+sqrt(I_(2)))^(2)`
The intensity of minima `I_(min) = (sqrt(I_(1))-sqrt(I_(2)))^(2)`
Given intensities are in the ratio `64: 1`, so `I_(1) = 64,I_(2)= 1`
` I_(max)/I_(min) = (sqrt(I_(1))+sqrt(I_(2)))^(2)/ (sqrt(I_(1))-sqrt(I_(2)))^(2)`
`=(sqrt(64)-sqrt(1))^(2)/(sqrt(64)-sqrt_(1))^(2)`
`(8+1)^(2)/(8-1)^(2)`
`81/49`
`I_(max):I_(min)=81:49`