Question

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

Answer 1

Correct Answer - B
`I_(max)=(sqrt(I))+sqrt(nI))^(2)`
`I_("min")=sqrt(sqrt(I)-sqrt(nI))^(2)`
`(I_("max")-I_("min"))/(I_(max)+I_("min"))=((sqrt(I)+sqrt(nI))^(2)-(sqrt(I)-sqrt(nI))^(2))/((sqrt(I)+sqrt(nI))^(2)+(sqrt(I)-sqrt(nI))^(2))`
`=(1+n+2sqrt(n)-1-n+2sqrt(n))/(1+n+2sqrt(n)+1+n-2sqrt(n))=(4sqrt(n))/(2+2n)=(2sqrt(n))/(1+n)`