The angular width of central maximum in a single slit diffraction pattern is `30^(@)`. The width of the slit is 1`mu`m. the slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observer on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e., distance between the centres of each slit )

Options

A. 75`mu`m
B. `100 mu m`
C. `25 mu`m
D. 50 `mu`m

Explanation

The conditon for formation of first minima at points `O_(1) and O_(2)` is,
`d sin theta = lambda`
[ d = width of the slit,` theta` = angle of diffraction]
or, `lambda = (d)/(2) [" since" theta = 30^(@)]`
The friangle width in Young's double slit experiment,
`beta = (lambdaD)/(d')`
or, `d' = (5000xx 10^(-10) xx 0.5)/(10^(-2)) = 2.5 xx 10^(-5) m = 25 mu m`
The option (C) is correct.