Wave Optics - Result Question 27
29. 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 $5000 \AA$ is incident on the slit. The first secondary maximum is observed at an angle of :
[2016]
(a) $\sin ^{-1}(\frac{1}{4})$
(b) $\sin ^{-1}(\frac{2}{3})$
(c) $\sin ^{-1}(\frac{1}{2})$
(d) $\sin ^{-1}(\frac{3}{4})$
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Answer:
Correct Answer: 29. (d)
Solution:
- (d) For the first minima,
$\theta=\frac{\eta \lambda}{a} \Rightarrow \sin 30^{\circ}=\frac{\lambda}{a}=\frac{1}{2}$ First secondary maxima will be at
$ \sin \theta=\frac{3 \lambda}{2 a}=\frac{3}{2}(\frac{1}{2}) \Rightarrow \theta=\sin ^{-1}(\frac{3}{4}) $
