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

`I=I_1+I_2+2sqrtI_1sqrtI_2 costheta`…..(1)
Applying eq.(1) when phase difference is `(pi)/(2)`
`I_(pi/2)=I+4I` `implies` ` I_(pi/2)``=5I`
Again applying eq. (1) when d phase difference is `pi`
`I_pi=I+4I+2sqrtIsqrt4Icospi`
:' `I_pi=I` :' 'I_(pi/2)-I_pi=4I`