In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of $30{^\circ}.$ The direction $ heta$ of the first secondary maximum is given by

Question

In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of $30{^\circ}.$ The direction $	heta$ of the first secondary maximum is given by

Dr. Abubacker · Accepted Answer

(b) For first diffraction minimum
$a\sin	heta = \lambda$
$\Rightarrow a = \frac{\lambda}{\sin	heta}$
For first secondary maximum
$a\sin{	heta'} = \frac{3\lambda}{2}$
Or $\sin{	heta'} = \frac{3\lambda}{2} 	imes \frac{1}{a} = \frac{36\lambda}{2} 	imes \frac{\sin	heta}{\lambda}$
$= \frac{3}{2} 	imes \sin{30{^\circ} = \frac{3}{4}}$
Or $	heta^{'} = \sin^{- 1}\left( \frac{3}{4} ight)$

Q. In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of $30{^\circ}.$ The direction $\theta$ of the first secondary maximum is given by

Explanation

Reviewed by Dr. Abubacker

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