Two beams of ligth having intensities I and 4I interface to produce a fringe pattern on a screen. The phase difference between the beams is `(pi)/(2)` at point A and `pi` at point B. Then the difference between the resultant intensities at A and B is

Options

A. 2 I
B. 4 I
C. 5 I
D. 7 I

Answer

b

Explanation

We know that the resultant amplitude of two interfering waves is given by `R^(2) = a^(2) + B^(2) + 2a b cos phi`, where R is the amplitude of resultant wave, a is the amplitude of one wave, b is the amplitude of second wave, and `phi` as the phase difference between the two wave at a point.
Also
`I prop ("amplitude")^(2)`
`:. I prop I_(1) + I_(2) + 2sqrt I_(1) sqrt I_(2) cos phi`
Applying Eq. (i) when phase diffenence is `pi // 2`
`I_(pi // 2) prop I + 4 I`
`implies I_(pi // 2) prop 5 I`
Again, applying Eq. (i) when phase difference is `pi`
`I_(pi) prop I + 4 I + 2 sqrt I sqrt( 4I) cos pi`
`:. I_(pi) prop I implies I_(pi//2) - I_(pi) prop 4 I`
Correct option is (b)