A parallel beam of monochromatic light of wavelength `5000Å` is incident normally on a single narrow slit of width `0.001mm`. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to

Options

A. `0^(@)`
B. `15^(@)`
C. `30^(@)`
D. `60^(@)`

Answer

C

Explanation

Here, `lambda = 5000 Å = 5 xx 10^(-7)m`,
`a = 0.001 mm = 10^(-6)m`
For first minimum, `(n = 1)`
`a sin theta = n lambda = 1 lambda`
`sin theta = (lambda)/(a) = (5 xx 10^(-7))/(10^(-6)) = 0.5`,
`theta = 30^(@)`