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. 51 and I
B. 5 I and 31
C. 9 I and I
D. 9 I and 3 I

Answer

C

Explanation

Intensity ` propto (Amplitude)^(2)`
I`prop A^(2)`
When two waves (beams) of amplitude `A_(1)` and `A_(2)` superimpose, at maxima and minima, the amplitude of the resulting wave are (`A_(1) + A_(2) `) and (`A_(1) - A_(2) `) respectively. If the maximum and minimum possible intensities are `l_(max)` and `l_(min)` respectively, then
`l_(max) prop (A_(1)+A_(2))^(2)`
`l_(min) prop (A_(1)-A_(2))^(2)`
`l_(max)/l_(min)=[A_(1)+A_(2)/A_(1)-A_(2)]^(2) ={(A_(1)/A_(2) +1)/(A_(1)/A_(2) -1)}^(2)`, Where`A_(1)/A_(2)=sqrtI/sqrt4I=1/2`
`l_(max)/L_(min)=9/2implies l_(max)=91, l_(mi n=1)`
Hence (C) is correct.