The angular width of the central maximum in a single slit diffraction pattern is `60^(@)`. 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 observed 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. `25 mu m`
B. `50 mu m`
C. `75 mu m`
D. `100 mu m`

Answer

A

Explanation

`2 theta=60^(@)`
`:. theta=30^(@)`
For fringe of first order minimum
`d sin theta= lambda`
`:. d sin 30^(@) lambda,`
`:. Dxx(1)/(2)= lambda`
`:. lambda=(d)/(2)`
Width of fringe `beta=(lambdaD)/(d.)`
`d.=(lambdaD)/(beta)`
`=(d)/(2)xx(D)/(beta)`
`=(10^(-6))/(2)xx(50xx10^(-2))/(1xx10^(-2))`
`=25xx10^(-6)m`
`:.d.=25 mum`