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

Options

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

Answer

B

Explanation

`(I_("max") - I_("min"))/(I_("max") + I_("min")) = ((a _(1) + a_(2))^(2) - (a_(1) - a_(2))^(2))/((a_(1) + a_(2))^(2) + (a_1-a_2)^2)`
[`:'I_max=(a_1+a_2)^2,I_min=(a_1-a_2)^2` where a = amplitude]
`=(4a_1a_2)/(2(a_1^2+a_2^2))=(2a_1a_2)/(a_1^2+a_2^2)`
Now, dividing the numerator and denominator by `a_1a_2`, we get
`(I_max-I_min)/(I_max+I_min) =2/([(a_1)/a_2+a_2/a_1])=2/([sqrtalpha+1/sqrtalpha])=(2sqrtalpha)/((alpha+1))`