An initially parallel cylindrical beam travels in a medium of refractive index `mu(I)=mu_(0)+mu_(2)I,` where `mu_(0)` and `mu_(2)` are positive constants and `I` is the intensity of the light light beam. The intensity of the beam is decreasing with increasing radius.
At two points `P` and `Q` on a screen in Young's double slit experiment, waves from slits `S_(1)` and `S_(2)` have a path difference of `0` and `(lambda)/(4)` respectively. The ratio of intensities at `P` and `Q` will be :

Options

A. `3:2`
B. `2:1`
C. `sqrt(2):1`
D. `4:1`

Answer

B

Explanation

At `P:Deltax=0,Deltaphi=(2pi)/(lamda)xx0=0`
`I_(P)=(sqrt(I)+sqrt(I))^(2)=4I`
at `Q:Deltax=(lamda)/(4)`
`I_(Q)=I+I+2sqrt(II)cos((pi)/(2))=2I,(I_(P))/(I_(Q))=(4I)/(2I)=(2)/(1)`