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

Answer

B

Explanation

Here, `I_(1) = I, I_(2) = 4I, theta_(1) = pi//2, theta _(2) = pi`
Resultant intensity `I_(theta_(1)) = I_(1)+I_(2) + 2sqrt(I_(1)I_(2))cos theta_(1)`
`= I+4I+2sqrt(Ixx4I)cos pi//2 = 5I`
Resultant intensity `I_(theta_(1)) = I_(1)+I_(2)+2sqrt(I_(1)I_(2))cos theta_(2)`
`= I+4I+2sqrt(1xx4I)cos pi`
`= 5I-4I=I :. I_(theta_(1))-I_(theta_(2)) = 5I - I = 4I`