Question

A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observe on 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.

Answer 1

Wavelength of light beam , `lambda=500 nm =500xx10^(-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 form the centre of the screen can be obtained as :
`x=2.5 mm =2.5xx10^(-3)m.`
It is related to the order of minima as :
`nlambda=x(d)/(D)`
`d=(nlambdaD)/(x)`
`=(1xx500xx10^(-9)xx1)/(2.5xx10^(-3))=2xx10^(-4)m=0.2mm`
Therefore, the width of the slits is 0.2 mm