The two coherent sources with intensity ratio `beta` produce interference. The fringe visibility will be

Options

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

Answer

A

Explanation

`(I_(1))/(I_(2))=(a^(2))/(b^(2))=beta:.(a)/(b)=sqrt(beta)`
Fringe visibility is given by
`V=(I_("max")-I_("min"))/(I_("max")+I_("min"))=((a+b)^(2)-(a-b)^(2))/((a+b)^(2)+(a-b)^(2))`
`=(4ab)/(2(a^(2)+b^(2)))=(2(a//b))/(((a^(2))/(b^(2))+1))=(2sqrt(beta))/(beta+1)`