Figure shows two coherent sources `S_(1)` and `S_(2)` emitting wavelength `lambda`. The separation `S_(1) S_(2) = 1.5 lambda` and `S_(1)` is ahead in phase by `pi // 2` relative to `S_(2)` Then the maxima occur in direction `theta` given by `sin^(-1)` of
(i) 0 (ii) `1// 2` (iii) `-1//6` (iv) `-5 // 6`
Correct option are

Options

A. (ii), (iii), and (iv)
B. (i), (ii), and (iii)
C. (i), (iii), and (iv)
D. All the above

Answer

a

Explanation

`delta =` phase differene between the waves from `S_(1)` and `S_(2)` at `P = `
`(pi)/(2) - (2 pi)/(2) (d sin theta)`
For maximum intensity at P, `delta = nx` where `n = 0, +- 1, +- 2`......
`:. (2pi)/(2) (1.5 lambda sin theta) (pi)/(2) = n pi`
`implies n - (1)/(2) = 3 sin theta`
`implies sin theta = ((n - (1)/(2))/(3))`
For `n = 0`, `sin theta = -(1)/(6)`
For `n = +- 1` `sin theta = (1)/(6), - (1)/(2)`
For `n = +- 2`, `sin theta = (1)/(2) , -(5)/(6)`