In deriving the single slit diffraction pattern,
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.

Solution:

Let “a”  be the width of a single slit. The single slit is further divided into n smaller slits of width a’.

a’ = a/n

Each of the smaller slits should produce zero intensity for the single slit to produce zero intensity.

For this to happen, the angle of diffraction, θ = λ/a’

⇒ θ  = λ/(a/n)

or, θ = nλ/a

Therefore, in deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a.

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