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,phi_(1)=-(pi)/(2),phi_(2)=pi`
`I_(A)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi_(1)`
`=I+4I+2sqrt(Ixx4I)cos.(pi)/(2)=5l`
`I_(B)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi_(2)`
`=I+4I+2sqrt(I4I)cospi=5I-4I=I`
`:.I_(A)-I_(B)=5I-I=4I`