Two beams of light having intensities I and 4I interfere 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

`I (phi) = I_(1) + I_(2) + 2 sqrt(I_(1) I_(2)) cos phi`
Here,
`I_(1) = I` and `I_(2) = 4 I`
At point A,
`phi = (pi)/(2)`
`:. I_(A) = I + 4 I = 5 I`
At point B,
`phi = pi`
`:. I_(B) = I + 4 I - 4 I = I`
`:. I_(A) - I_(B) = 4 I`