Interference fringes are produced on a screen by using two light sources of intensities / and 9/. The phase difference between the beams `pi/2` is at point P and `pi`at point Q on the screen. The difference between the resultant intensities at point P and Q is

Options

A. 2I
B. 4I
C. 6I
D. 8I

Answer

C

Explanation

According to question, resultant intensity of interferring wave is given by
`I_(P)=I_(1)+I_(2)+2sqrt(I_(1)I_(2)cos phi)`
For `phi=(pi)/(2), I_(P)=I+9I=10I`
Again at point Q, resultant intensity is given by
`I_(Q)=I_(Q)=I_(1)+I_(2)+2sqrt(I_(1)I_(2)cos phi)`
For `phi=pi, I_(Q)=I+9I+(-2sqrt(9(I)^(2)))`
`=10I-6I=4I`
Now, difference between the resultant intensity is given by
`Delta I=I_(P)-I_(Q)=10I-4I=6I`