Two coherent sources of intensity ratio `beta` interfere, then `(I_(max)-I_(min))/(I_(max)+I_(min))` is

Options

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

Answer

D

Explanation

`(I_(1))/(I_(2)) = beta = (a^(2))/(b^(2)) :. (a)/(b) = sqrt(beta)`
`I_(max) = (a + b)^(2)`
`I_(min) = (a - b)^(2)`
`(I_(max) - I_(min))/(I_(max) + I_(min)) = ((a + b)^(2) - (a - b)^(2))/((a + b)^(2) + (a - b)^(2)) = (4 ab)/(2(a^(2) + b^(2)))`
`= (2 ab)/((a^(2) + b^(2))) = (2b.b sqrt(beta))/(b^(2) + betab^(2)) = (2sqrt(beta))/(1 + beta)`