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.
Wavelength of light beam, λ = 500 nm = 500 × 10−9 m`
Distance of the screen from the slit, D = 1 m
For first minima, n = 1
Distance between the slits = d
Distance of the first minimum from the centre of the screen can be obtained as:
x = 2.5 mm = 2.5 × 10−3 m
It is related to the order of minima as:
`nlambda = x d/D`
`d = (nlambdaD)/x`
`= (1xx500 xx 10^(-9) xx 1)/(2.5 xx10^(-3)) = 2xx10 ^(-4) m = 0.2 mm`
Therefore, the width of the slits is 0.2 mm.