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. `I_(1) + I_(2)`
B. `(sqrt(I_(1)) + sqrt(I_(2)))^(2)`
C. (c ) `(sqrt(I_(1)) - sqrt(I_(2)))^(2)`
D. `2(I_(1) + I_(2))`

Answer

D

Explanation

In interference, resultant intensity is
`I = I_(1) + I_(2) + 2sqrt(I_(1)I_(2)) cos phi`
`I_(max) = I_(1) + I_(2) + 2sqrt(I_(1)I_(2)) cos 0^(@)`
`= I_(1) + I_(2) + 2sqrt(I_(1)I_(2))`
`I_(min) = I_(1) + I_(2) + 2sqrt(I_(1)I_(2)) cos 180^(@)`
`= I_(1) + I_(2) - 2sqrt(I_(1)I_(2))`
`I_(max) + I_(min) = 2 (I_(1) + I_(2))`