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 $5000 \mathring A$ is incident on the slit. The first secondary maximum is observed at an angle of :

• A. $\sin^{-1} \left( \frac{2}{3} \right)$
• B. $\sin^{-1} \left( \frac{1}{2} \right)$
• C. $\sin^{-1} \left( \frac{3}{4} \right)$
• D. $\sin^{-1} \left( \frac{1}{4} \right)$

Answer 1

Answer: (C)

$\sin^{-1} \left( \frac{3}{4} \right)$

Answer 2

For first minima , $\sin 30^{\circ} = \frac{\lambda}{a} = \frac{1}{2}$
First secondary maxima will be at
$\sin \theta = \frac{3 \lambda}{2a} = \frac{3}{2} \left( \frac{1}{2} \right) \, \Rightarrow \, \theta = \sin^{-1} \left( \frac{3}{4} \right)$