`S_1 and S_2` are two coherent sources of radiations separated by distance `100.25 lambda`, where `lambda` is the wave length of radiation. `S_1` leads `S_2` in phase by `pi//2`.A and B are two points on the line joining `S_1 and S_2` as shown in figure.The ratio of amplitudes of component waves from source `S_1 and S_2` at A and B are in ratio 1:2. The ratio of intensity at A to that of B `(I_A/I_B)` is

Options

A. `oo`
B. `1/9`
C. 0
D. 9

Explanation

For interference at A:`S_2` is behind of `S_1` by a distance of `100lambda+lambda/4`.(equal to phase difference `pi/2`).Further `S_2` lags `S_1` by `pi/2` Hence the waves from `S_1 and S_2`interfere at A with a phase difference `200.5pi+0.5pi=201pi=pi`
Hence the net amplitude at A is 2a-a=a
For interference at B :`S_2` is ahead of `S_1` by a distance of `100lambda+lambda/4`.(equal to phase difference `pi/2`).Further `S_2` lags `S_1` by `pi/2`
Hence waves from `S_1 and S_2` interfere at B with a phase difference of `200.5 pi-0.5pi=200pi=0pi`.
Hence the net amplitude at A is 2a+a=3a
Hence `(I_A/I_B)=(a/(3a))^2=1/9`