In a diffraction pattern due to single slit of width ' a ', the f… - Vidyadip

MCQ

In a diffraction pattern due to single slit of width ' $a$ ', the first minimum is observed at an angle $30^{\circ}$ when the light of wavelength 5400 Å is incident on the slit. The first secondary maximum is observed at an angle of $\left(\sin 30^{\circ}=\frac{1}{2}\right)$

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

✓

Answer

(a) : For first minimum, $a \sin \theta=\lambda$
$
\begin{aligned}
& \theta=30^{\circ}, a \sin 30^{\circ}=\lambda \\
& a=2 \lambda......(i)
\end{aligned}
$
For first secondary maximum, $a \sin \theta^{\prime}=\frac{3}{2} \lambda$
$
2 \lambda \sin \theta^{\prime}=\frac{3}{2} \lambda ; \sin \theta^{\prime}=\frac{3}{4} \Rightarrow \theta^{\prime}=\sin ^{-1}\left(\frac{3}{4}\right)
$

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