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:
Consider that a single slit of width d is divided into n smaller slits.
$\therefore$ Width of each slit, $d^{\prime}=\frac{d}{n}$
Angle of diffraction is given by the relation,
$\theta=\frac{\frac{d}{d^{\prime}} \lambda}{d}=\frac{\lambda}{d^{\prime}}$
Now, each of these infinitesimally small slit sends zero intensity in directionθ. Hence, the combination of these slits will give zero intensity.