Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Options

A. 5 I and I
B. 5 I and 3 I
C. 9 I and I
D. 9 I and 3 I

Answer

C

Explanation

`I_("max") = (sqrt(I_(1)) + sqrt(I_(2)))^(2) = (sqrt(4I) + sqrt(I))^(2) = 9I`
`I_("min") = (sqrt(I_(1)) - sqrt(I_(2)))^(2) = (sqrt(4I) - sqrt(I))^(2) = I`