A parallel beam of light of wavelength 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 minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.
The relation between fringe width “x” and the order of minima “n” is given as:
or
where,
d = width of the screen
D = distance between the screen and the slit
n = order of minima
λ = wavelength of the light
Given,
λ = 500 nm = 500 × 10 - 9 m
Distance between the screen and the slit , D = 1 m
For first minima, n = 1
x = 2.5 mm = 2.5 × 10 - 3 m
Distance between the slits = d
Distance of the first minimum from the centre of the screen can be obtained as:
⇒ d = 2 × 10 - 4 m = 0.2 mm
Therefore, the width of the slits is 0.2 mm.