Two coherent sources of intensity ratio `alpha ` interface . In interference pattern `(I_("max") - I_("min"))/(I_("max") + I_("min")) = `

Options

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

Answer

B

Explanation

`(I_(1))/(I_(2))=(alpha)/(1)`
`:. I_(1)= alph I_(2)`
`(I_("max")-I_("min"))/(I_("max")+I_("min"))=((sqrt(I_(2))+sqrtI_(2))^(2)-(sqrt(I_(2))-sqrt(I_(2)))^(2))/((sqrt(I_(1))+sqrt(I_(2)))^(2)+(sqrt(I_(1))+sqrt(I_(2)))^(2))`
`=((sqrt(alphaI_(2))+sqrt(I_(2)))^(2)-(sqrt(alphaI_(2))-sqrt(I_(2)))^(2))/((sqrt(alphaI_(2))+sqrt(I_(2)))^(2)+(sqrt(alphaI_(2))-sqrt(I_(2)))^(2))`
`=(2sqrt(alpha))/(1+alpha)`