The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference patten, the ratio `(I_(max)-I_(min))/(I_(max)+I_(min))` will be

Options

A. `(sqrt(n))/((n+1)^(2))`
B. `(2sqrt(n))/((n+1)^(2))`
C. `(sqrt(n))/(n+1)`
D. `(2sqrt(n))/(n+1)`

Answer

D

Explanation

Let `(I_(1))/(I_(2)) = (n)/(1)`
`(I_("max") - I_("min"))/(I_("max") = I_("min")) = ((sqrt(I_(1)) + sqrt(I_(2)))^(2) - (sqrt(I_(1)) - sqrt(I_(2)))^(2))/((sqrt(I_(1)) + sqrt(I_(2)))^(2) + (sqrt(I_(1)) - sqrt(I_(2)))^(2)) = (4sqrt(I_(1)I_(2)))/(2(I_(1) + I_(2)))`
Dividing numerator and denominator by `I_(2)`.
Required ratio will be `= (2sqrt((I_(1))/(I_(2))))/(((I_(1))/(I_(2)) + 1)) = (2sqrt(n))/(n+1)`