In a diffraction pattern due to a single slit of width $a$, the first minimum is observed at an angle $30^\cir

Question

In a diffraction pattern due to a single slit of width $a$, the first minimum is observed at an angle $30^\circ$ when light of wavelength $5000	ext{ \AA}$ is incident on the slit. The first secondary maximum is observed at an angle of

Accepted Answer

For a single slit diffraction pattern, the condition for the $n^{	ext{th}}$ minimum is given by $a \sin	heta = n\lambda$.
For the first minimum ($n = 1$), $	heta = 30^\circ$:
$a \sin 30^\circ = 1 \cdot \lambda$
$a \left(\frac{1}{2}ight) = \lambda \implies a = 2\lambda$
The condition for the $n^{	ext{th}}$ secondary maximum is $a \sin	heta' = \left(n + \frac{1}{2}ight)\lambda$.
For the first secondary maximum ($n = 1$):
$a \sin	heta' = \frac{3\lambda}{2}$
Substitute $a = 2\lambda$ into the equation:
$(2\lambda) \sin	heta' = \frac{3\lambda}{2}$
$\sin	heta' = \frac{3}{4}$
$	heta' = \sin^{-1}\left(\frac{3}{4}ight)$

Step-by-Step Solution

Practice All PHYSICS Questions