In an interference the intensity of two interfering waves are I and 4I respectively. They produce intensity at two point A and B with phase angle of `(pi)/(2)` and `pi` it respectively. Then differation in between them is ......

Options

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

Answer

C

Explanation

Resultant intensity `I=I_(1)+I_(2)+2 sqrt(I_(1)I_(2)) cos phi`
Here `I_(1)=I`
and `I_(2) =4I, phi_(1)=(pi)/(2), phi_(2)= pi`
On point `A I_(A)=I+4I+2 sqrt(4I^(2)) "cos" (pi)/(2)`
On point `B I_(B)=I+4I+2 sqrt(4I^(2)) "cos" pi`
`=5I-4I`
=I
Now `I_(A)-I_(B)=5I-I=4I`