In experimental set up of interference the twol interfering sources `S_(1) and S_(2)` have an initial phase difference corresponding to a path difference of `lambda//4`. The phase difference due to path difference between the twoll interfering waves at a point of constructive and destructive interference respectively is

Options

A. `(2n-1)(pi)/(2),(2n+1) pi`
B. `(2n-1)pi,(2n+1) (pi)/(2)`
C. `(2n-1)pi,(2n+1//2) pi`
D. `(2n+1//2)pi, (2n-1//2)pi`

Answer

D

Explanation

For path diff. `=(lambda)/(4)`
Phase diff. `=(2pi )/(lambda)=(lambda)/(4) =(pi)/(2)`
Thus, initial phase difference between the wves equal to `pi//2`
For constructive interference,
Phase diff ` =2pi n+ pi + pi //2 =(2n-1//2) pi`
For destructive interference,
Phase diff. `(2n-1)pi + pi //2 =(2n-1//2)pi`