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

Answer: (A)

$\pi radian$

Answer 2

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
$\Delta \Phi = \frac{ 2 \pi }{ \lambda } \Delta x = \frac{2 \pi }{ \lambda } \times \frac{\lambda}{ 2} = \pi$