A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minima is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.
The distance of the nth minima from the centre of the screen is given by
$x_{ n }$ = nDλ/a
Where D = distance of slit form screen = 1m
λ = wavelength of the light = 500nm
= 500 x ${{10}^{-9}}$ m,
n=1
$x_{ n }$ = 2.5 mm = 2.5 x ${{10}^{-3}}$ m,
and a = width of the slit first minima=?
puting these values we get
2.5 x ${{10}^{-3}}$ = 500 x ${{10}^{-9}}$/a
====> a = 2 x ${{10}^{-4}}$ m = 0.2 m