The interference pattern is obtained with two coherent light sources of intensity ration n. In the interference pattern, 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

It is given that, `I_(2)/I_(1)=nrArrI_(2)=nI_(1)`
`:.` Ratio of intensities is given by
`(I_(max)-I_(min))/(I_(max)+I_(min))=((sqrtI_(2)+sqrt(I_(1)))^(2)-(sqrt(I_(2)-I_(1)))^(2))/((sqrt(I_(1))+sqrt(I_(2)))^(2)+(sqrt(I_(2))-sqrt(I_(1)))^(2))`
`=((sqrt(I_(2)/I_(1))+1)^(2)-(sqrt(I_(2)/I_(1))-1)^(2))/((sqrt(I_(2)/I_(1))+1)^(2)+(sqrt(I_(2)/I_(1))-1)^(2))`
`=((sqrt(n)+1)^(2)-(sqrt(n)-1)^(2))/((sqrt(n)+1)^(2)+(sqrt(n)-1)^(2))=(2sqrt(n))/(n+1)`