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 minimum is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.

Explanation

Wavelength of incident light, `lambda = 500 nm = 500 xx 10^(-9) m` distance between slit and screen, D = 1 m
For 1st minima angular width on either side of central maxima =`(lambda)/(a)`
`therefore " " (lambda)/(a). D = 2.5 xx 10^(-3) m `
a = ` (lambda.D)/(2.5 xx 10^(-3)) = (500xx10^(-9)xx1)/(2.5 xx 10^(-3))`
`= 2xx 10^(-4)m = 0.2 mm `