At the first minimum adjacent to the central maximum of a single-slit diffraction pattern the phase difference between the Huygens wavelet from the edge of the slit and the wavelet from the mid-point of the slit is

Options

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

Answer

A

Explanation

The situation is shown in the figure.

In figure A and B represent the edges of the slit AB of width a and C represents the midpoint of the slit. For the first minimum at P,
`asintheta=lambda` ...(i)
where `lambda` is the wavelength of light.
The path difference between the wavelets from A to C is
`Deltax=(a)/(2)sintheta=(1)/(2)(asintheta)=(lambda)/(2)` (using (i))
The corresponding phase difference `Deltaphi` is
`Deltaphi=(2pi)/(lambda)Deltax=(2pi)/(lambda)xx(lambda)/(2)=pi`