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. `25mum`
B. `50mum`
C. `75mum`
D. `100mum`

Answer

A

Explanation

Angular width of central maxima = `(2lamda)/d`
or, `lamda=d/2`, Fringe width, `beta=(lamdaxxD)/(d.)`
`10^(-2)=d/2xx(50xx10^(-2))/(d.)=(10^(-6)xx50xx10^(-2))/(2xxd.)`
Therefore, slit separation distance, d. = `25mum`