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_("min"))=((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2))))^(2)implies16/1=((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2))))^(2)`
`implies(sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2)))=4/1impliessqrt(I_(1))+sqrt(I_(2))=4sqrt(I_(1))-4sqrt(I_(2))`
`implies5sqrt(I_(2))=3sqrt(I_(1))implies(I_(1))/(I_(2))=25/9`