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. `9I`

Answer

B

Explanation

`DeltaI=(I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi_(1))-(I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi_(2))`
`=2sqrt(I_(1)I_(2))(cosphi_(1)-cosphi_(2))=2xx2I("cos"phi/2-cospi)=4I`