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

Options

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

Answer

A

Explanation

`(I_(1))/(I_(2))=(alpha)/(1)`
`:.I_(1)=alphaI_(2)`
`=((sqrtI_(1)+sqrtI_(2))^(2)-(sqrtI_(1)-sqrtI_(2))^(2))/((sqrtI_(1)+sqrtI_(2))^(2)+(sqrtsqrtI_(1)+sqrtI_(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))`
`=(2sqrtalpha)/(1+alpha)`