Question

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

Answer 1

Consider that a single slit of width $a$ is divided into $n$ smaller slits, then width of each smaller slit will be.
$a^{\prime }=\frac{a}{n}$
Now the angle of diffraction for each such slit will be
$\theta =\frac{n\lambda }{a}$
$\theta =\frac{\lambda }{a^{\prime }}$
Now, intensity of light due to each of these infinitesimally small slits will be zero in the direction $\theta$.
Hence, the combination of these slits will give zero intensity.