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

Q10.21    In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of \frac{n\lambda}{a}. Justify this by suitably dividing the slit to bring out the cancellation.

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Let the width of the slit b be divided into n equal parts so that 

b'=\frac{b}{n}

b=b'n

Now,

\theta=\frac{n\lambda}{b}=\frac{n\lambda}{b'n}=\frac{\lambda}{b'}

At this angle, each slit will make the first diffraction minimum. therefore the resultant intensity for all the slits will be zero at the angle of \frac{n\lambda}{b}.

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