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 $5000\,Å$ 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)

For first minima, $sin30^\circ =\frac{\lambda }{a}=\frac{1}{2}$
First secondary maxima will be at
$sin\theta =\frac{3 \lambda }{2 a}=\frac{3}{2}\left(\frac{1}{2}\right)\Rightarrow \theta =sin^{- 1}\left(\frac{3}{4}\right)$