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 3I
C. 4I and I
D. 9I and I

Answer

D

Explanation

We know that,
Maximum intensities,
`I_("max")=(sqrt(I_(1))+sqrt(I_(2)))^(2) " "`…(i)
Minimum intensities,
`I_("min")=(sqrt(I_(1))-sqrt(I_(2)))^(2) " "`…(ii)
So, the ratio of the maximum and minimum of intensities is
`(I_("max"))/(I_("min"))=((sqrt(I_(1))+sqrt(I_(2)))^(2))/((sqrt(I_(1))-sqrt(I_(2)))^(2))`
`rArr (I_("max"))/(I_("min"))=((sqrt(4I)+sqrt(I))^(2))/((sqrt(4I)-sqrt(I))^(2))=((3sqrt(I))/(sqrt(I)))^(2)=(9)/(1)=9:1`