For a parallel beam of monochromatic light of wavelength `'lambda'` differaction is produced by a single slit whose width `'a'` is of the order as wavelength of the light. If `'D'` is the distance of the screen from the slit, the width of the central maxima will be

Options

A. `(D lambda)/`
B. `(D a)/(lambda)`
C. `(2 D a)/(lambda)`
D. `(2 D lambda)/(a)`

Answer

D

Explanation

As angular width, `theta = (lambda)/(a)`

In Fig.
`2 theta = (arc)/(radius) ~~ ("Linear width")/(D)`
`:.` Linear width of central maxima `= 2 D theta`
width of central maxima `= (2 D lambda)/(a)`