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The interference pattern is obtained wit...

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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Knowledge Check

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