Two periodic waves of intensities `I_(1)` and `I_(2)` pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

Options

A. `(sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(II_(2)))`
B. `sqrt(I_(1)^(2)+I_(2)^(2))/sqrt(I_(1)^(2)-I_(2)^(2))`
C. `(sqrt(I_(1))-sqrt(I_(2)))/(sqrt(I_(1))+sqrt(I_(2)))`
D. `((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2))))^(2)`

Answer

D

Explanation

Resultant Intensity due to coherent source is given by
`l_("max") = l_(1) + l_(2) + 2sqrt(l_(1)l_(2) cos phi)`
`l_("max") = (sqrtl_(1) + sqrtl_(2))^(2)`
and `l_("min") = (sqrtl_(1) - sqrtl_(2))^(2)`
The Ratio of the maximum and minimum
`= ((sqrtl_(1) + sqrtl_(2))^(2))/((sqrtl_(1) - sqrtl_(2))^(2)) = ((sqrtl_(1) + sqrtl_(2))/(sqrtl_(1) - sqrtl_(2)))^(2)`