Fig, here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20m. The separation PQ si 5m, and phase of P is ahead of the phase Q by `90^(@)`. A, B and C are three distant points of observation equidistant from the mid - point of PQ. The intensity of radiations of A, B, C will be in the ratio

Options

A. `0:1:4`
B. `4:1:0`
C. `0:1:2`
D. `2:1:0`

Answer

D

Explanation

At `A: PA-QA=PQ=5m=20/4=lambda/4=Deltax`
`phi^(')=(2pi)/lambdaDeltax=(2pi)/lambda.lambda/4=pi/2`
Phase of `Q` is greater by`(90^(@)=pi/2)`than `P`.
Net phase difference `phi=pi//2-pi//2=0`
`I_(A)=4I^(')`
At `B: phi=90^(@)=pi//2`
`I_(B)=2I^(')`
At `C: Deltax=QA-PA=lambda//4, phi^(')=pi//2`
Net phase difference `f=phi=pi//2+pi//2=pi`
`I_(C)=0`
`I_(A):I_(B):I_(C)=4I^('):2I^('):0=2:1:0`