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
That maximum intensity `I_(max)=(sqrt(I_(1))+sqrt(I_(2)))^(2).....(i)`
The minimum intensity `I_(min)=(sqrt(I_(1))-sqrt(I_(2)))^(2) ....(ii)`
So, the ratio of the maximum and minimum intensities is
`I_(max)/I_(min)=(sqrt(I_(1))+sqrt(I_(2)))^(2)/((sqrt(I_(1))-sqrt(I_(2)))^(2))=(sqrt(4I)+sqrt(I))^(2)/((sqrt(4I)-sqrt(I))^(2))`
`rArrI_(max)/I_(min)=((3sqrt(I))/(sqrt(I)))^(2)=9/1=9:1`
Hence, the maximum and minimum intensities intensible in the resulting pattern are 9I and I