Question

In a Fraunhofer diffraction at single slit of width $d$ with incident light of wavelength $5500 \mathring{A} $, the j first minimum is observed, at angle $30^{\circ}$. The first secondary maximum is observed at an angle $\theta =$

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

Answer 1

Answer: (C)

Slit width $= d $
$\lambda = 5500 \mathring{A} = 5.5 \times 10^{-7}m, \theta_{n} = 30^{\circ} $
For first secondary minima, $d sin\, \theta_{n} = \lambda $
$ d =\frac{\lambda}{sin\, \theta_{n}} = \frac{5.5 \times 10^{-7} }{sin\, 30^{\circ}} $
$ = 11\times 10^{-7} \,m $
For first secondary maxima, $d \,sin\, \theta_{n} = \frac{3\lambda}{2} $
i.e., $sin \,\theta_{n} = \frac{3\lambda}{2d}$
$ =\frac{3\times 5.5\times 10^{-7}}{2\times 11\times 10^{-7}} $
$ sin \,\theta_{n} = \frac{3}{4 }$ or
$\theta_{n} = sin ^{-1} \left(3/4\right)$