Two coherent sources produce waves of different intensities which interfere. A fter interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

Options

A. `25:9`
B. `16:9`
C. `5:3`
D. `4:1`

Answer

A

Explanation

`I_(maX.)/(I_(m in.))=((sqrtI_(1) + sqrtI_(2))/sqrt(I_(1) - sqrtI_(2)\))^(2)` `rArr` `(16)/(1)=((sqrtI_(1) + sqrtI_(2))/sqrt(I_(1) - sqrtI_(2)\))^(2)` `rArr` `((sqrtI_(1) + sqrtI_(2))/sqrt(I_(1) - sqrtI_(2)\)) = (4)/(1)`
`rArr` `sqrtI_(2) + sqrtI(2) = 4 sqrtI_(1) - 4 sqrtI_(2)` `rArr` `5sqrtI_(2) = 3 sqrtI_(1)` `rArr` `I_(1)/(I_(2)) = (25)/(9)`