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The interference pattern is obtained wit...

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

A

`(sqrt(n))/((n+1)^(2))`

B

`(2sqrt(n))/((n+1)^(2))`

C

`(sqrt(n))/(n+1)`

D

`(2sqrt(n))/(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `(I_(1))/(I_(2)) = (n)/(1)`
`(I_("max") -I_("min"))/(I_("max") + I_("min")) = ((sqrt(I_(1)) + sqrt(I_(2)))^(2)-(sqrt(I_(1))-sqrt(I_(2)))^(1))/((sqrt(I_(1))+sqrt(I_(2)))^(2)+(sqrt(I_(1)) + sqrt(I_(2)))^(2)) = (4sqrt(I_(1)I_(2)))/(2(I_(1) + I_(2)))`
Dividing numerator and denominator by `I_(1)`
Required ratio will be `= (2sqrt((I_(1))/(I_(2))))/(((I_(1))/(I_(2)) + 1)) = (2sqrt(n))/(n+1)`
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