The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference patten, the ratio `(I_(max)-I_(min))/(I_(max)+I_(min))` will be

Options

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

Answer

B

Explanation

Here, `(I_(1))/(I_(2))=n`
`(I_("max"))/(I_("min"))=((sqrt(I_(1))+sqrt(I_(2)))/(sqrtI_(1)-sqrtI_(2)))^(2)=((sqrt(I_(1)//I_(2))+1)/(sqrt(I_(1)//I_(2))-1))^(2)=((sqrt(n)+1)/(sqrt(n)-1))^(2)`
`(I_(max)-I_(min))/(I_(max)+I_(min))= ((I_(max))/(I_(min))-1)/((I_(max))/(I_(min))+1)`
`=(((sqrt(n)+1)/(sqrt(n)-1))^(2)-1)/(((sqrt(n)+1)/(sqrt(n)-1))^(2)+1)=((sqrt(n)+1)^(2)-(sqrt(n)-1)^(2))/((sqrt(n)+1)^(2)+(sqrt(n)-1)^(2))=(2sqrt(n))/(n+1)`