In deriving the single slit diffraction pattern, it was stated that th

1.	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» 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.

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»

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.

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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.

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