Question

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a. Justify this by suitably dividing the slit to bring out the cancellation.

Answer 1

Divide the slit of width an into n parts, so that the width of each small part of the slit is

a' = \(\frac{a}{n}\)

⇒ a = na'

For a path difference nλ between the waves from two extreme ends of the slit,

θ = \(\frac{n\lambda}{a}=\frac{n\lambda}{na'}= \frac{\lambda}{a'}\)

Each of the n parts of the slit will send zero intensity in the direction 0. Obviously, all the n parts together will also give zero intensity.