Question

In a single-slit diffraction pattern, the position of first secondary maximum is at $30^{\circ }$ , then what will be the angular position of second minima?

• A. $\left(\sin\right)^{- 1} \, \left(2 / 3\right)$
• B. $\left(\sin\right)^{- 1} \left(\right.1\left.\right) \, $
• C. $\left(\sin\right)^{- 1} \left(1 / 2\right)$
• D. None

Answer 1

Answer: (A)

For first secondary maxima,
$\sin\left(\theta \right)_{1}=\left(1 + \frac{1}{2}\right)\frac{\lambda }{a}=\frac{3 \lambda }{2 a}$ $\Rightarrow \sin30^{o}=\frac{3 \lambda }{2 a}$
$\Rightarrow \frac{\lambda }{a}=\frac{1}{3}$
For second minima,
$\sin \theta =\frac{2 \lambda }{a}=\frac{2}{3}$
or $\theta =\left(\sin\right)^{- 1} \, \left(2 / 3\right)$