Two coherent sources of intensity ratio `alpha` interfere. 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

Given: `(I_(1))/(I_(2))=alpha" "therefore I_(1)=I_(2)alpha`
`I_(max)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))`
and `I_("min")=I_(1)+I_(2)-2sqrt(I_(1)I_(2))`
`therefore (I_(Max)-I_("min"))/(I_("max")-I_("min"))=(4sqrt(I_(1)I_(2)))/(2(I_(1)+I_(2)))`
`=(2sqrt(I_(1)I_(2)))/((I_(1)+I_(2)))`
`=(2sqrt(I_(2)alpha*I_(2)))/(I_(2)alpha+I_(2))`
`=(2I_(2)sqrt(alpha))/(I_(2)(I+alpha))=(2sqrt(alpha))/(1+alpha)`