question_answer

In a single slit diffraction of light of wavelength l by a slit of width e, the size of the central maximum on a screen at a distance b is

A)            \[2b\lambda +e\]              

B)            \[\frac{2b\lambda }{e}\]

C)            \[\frac{2b\lambda }{e}+e\]   

D)            \[\frac{2b\lambda }{e}-e\]

Correct Answer: C

Solution :

           The direction in which the first minima occurs is \[\theta \] (say). Then \[e\sin \theta =\lambda \] or \[e\theta =\lambda \] or, \[\theta =\frac{\lambda }{e}\] \[(\because \,\,\,\theta =\sin \theta \] when \[\theta \] small) Width of the central maximum \[=2b\theta +e=2b.\frac{\lambda }{e}+e\]