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

Options

A. `(2 sqrt(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)`