At the first minimum adjacent to the central maximum of a single slit differation pattern the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the mid point of the slit is......

Options

A. `(pi)/(8)` rad
B. `(pi)/(4)` rad
C. `(pi)/(2)` rad
D. `pi` rad

Answer

D

Explanation

In right angle `DeltaS_(1)NS, sin theta=(SN)/(SS_(1))`
`sin theta=(dx_(1))/((a)/(2)) [ :. SS_(1)=(a)/(2)]`

`:. dx_(1)=(a)/(2) sin theta " "...(1)`
where `Deltax_(1)` is a path difference.
Now, for first minimum,
`a sin theta= lambda " " [d=a]`
`:. sin theta=(lambda)/(a) " "...(2)`
`:. Deltax_(1)=(a)/(2)xx(lambda)/(a)=(lambda)/(2)` [`:.` From equation (1) and (2)]
Now phase difference
`Delta phi_(1)=kxx` path difference
`=(2pi)/(lambda)xx deltax_(1)`
`=(2pi)/(lambda)xx(lambda)/(2)=pi` rad