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

Answer

B

Explanation

Maximum intensity
`I_(max)[sqrt(I_(1))+sqrt(I_(2))]^(2)=[sqrt(I)+sqrt(4I)]^(2)`
`=I+4I+2sqrt(I)sqrt(4I)=9I`
`I_("min")=[sqrt(I_(1))+sqrt(I_(2))]^(2)=[sqrt(I)-sqrt(4I)]^(2)`
`=I=4I-2sqrt(I)sqrt(4I)`
`therefore I_("minimum")=5I-4I=I`