Four identical coherent sourc e emiting monochromatic light if same wavelength lambda are placed at `A,B,C` and `D` as shown. Two receivers `R_(1)` and `R_(2)` are at but equal distance from B. The path difference between signals reaching from A&D at `R_(1)` is `(lambda)/(2)` and between signals reaching from A & B at `R_(2) is ~= 0`. Also assume that intensities of waves emitted by A,B,C &D reaching at `R_(1)` and `R_(2)` is same.

Options

A. `R_(1) `records greater intensity if all the sources are on.
B. `R_(1)`and`R_(2)` records same intensity if B is switched of, and other sources are on.
C. `R_(2)` records greater intensityif D switched off, and other sources are on.
D. It is possible to know, whether B is switch off or D is switched off by recording intensities at `R_(1)` and `R_(2)`

Answer

B, C, D

Explanation

At ` R_(2)`
`Delta Q_(BA) = Q _(BC)=0`
`Delta Q_(BD) = pi`
`At R_(1) `
`DeltaQ_(BA)=pi`
`Q_(AD)=pi`
`Delta Q_(BC)=pi`
`(A)` When all sources are on at `R_(1)`
`I=0`
at `R_(2)`,
`I prop 4a^(2)`
(where a is amptitude of individual waves reaching at `R_(1)` &`R^(2))`
`(B)` When only `B` is switched off
`I_(R_(1)) prop a^(2)`
`I_(R_(2))`
When only `D` is switched off
`I_(R_(1)) prop a^(2)`
`I_(R_(2)) prop 9a^(2)`
`(D)` By measuring intensities it is possible to know, which source out of `B & D` is switched off.