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

Options

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

Answer

D

Explanation

Let intensity of light be `I_(1) and I_(2)`
`:. (I_(1))/(I_(2))=n`
`(A_(1)^(2))/(A_(2)^(2))=n " " [ :. I prop A^(2)]`
`:.(A_(1))/(A_(2))= sqrt(n)`
Taking componendo and dividendo
`(A_(1)+A_(2))/(A_(1)-A_(2))=(sqrt(n)+1)/(sqrt(n)-1)`
`:. ((A_(1)+A_(2))^(2))/((A_(1)-A_(2))^(2))=(n+2sqrt(n)+1)/(n-2sqrt(n)+1)`
`:. (I_("max"))/(I_("min"))=(n+2sqrt(n)+1)/(n-2sqrt(n)+1)`
Taking componendo and dividendo again
`(I_("max")-I_("min"))/(I_("max")-I_("min))=(n+2sqrt(n)+1-n+2sqrt(n)+1)/(n+2sqrt(n)+1+n-2sqrt(n)+1)`
`=(4sqrt(n))/(2(n+1))=(2sqrt(n))/(n+1)`