Question

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

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

Answer 1

Answer: (D)

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

For first minima: $sin{30}^0=\frac{\lambda }{a}=\frac{1}{2}$

First secondary maxima will be at:

$sin\theta =\frac{3\lambda }{2a}=\frac{3}{2}\times \frac{1}{2}$

$\Rightarrow \theta =si{n}^{-1}\left(\frac{3}{4}\right)$