A monochromatic light of wavelength 500 nm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern. Find the angular width of the central maximum obained on the screen.
Estimate the number of fringes obatined in Young's double slit experiment with fringe width 0.5 mm, which can be accommodated within the region of total angular spread of the central maximum due to single slit.

Explanation

`lambda` = 500 nm = `5 xx 10^(-7)` m,
a = 0.2 mm = `2xx 10^(-4)`m
Angular width of central maxima,
`theta_(0) = (2lambda)/(a) = (2xx5xx10^(-7))/(2xx10^(-4)) = 5 xx 10^(-3) ` rad
The fringe width in Young's double slit experiment,
`beta = 0.5 mm = 5 xx 10^(-4)`m
The number of fringes obtained,
`N = (theta_(0) D)/(beta) = (5 xx 10^(-3) xx 1)/(5 xx 10^(-4)) = 10` [ assuming D = 1 m ]