Question

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

• A. $ \pi radian $
• B. $ \frac{\pi}{8} radian $
• C. $ \frac{\pi}{4} radian $
• D. $ \frac{\pi}{2} radian $

Answer 1

The Correct Option is A

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,
$ a sin \theta = \lambda $ $\hspace36mm$ ..............(i)
where A is the wavelength of light.
The path difference between the wavelets from
to C is
$\Delta x = \frac{a}{2} sin \theta = \frac{1}{2} (a sin \theta) $
$= \frac{ \lambda }{2}$ $\hspace26mm$ (using (1))
The corresponding phase difference $ \Delta \Phi $ is
$\Delta \Phi = \frac{ 2 \pi }{ \lambda } \Delta x = \frac{2 \pi }{ \lambda } \times \frac{\lambda}{ 2} = \pi $