CBSE Class 12 · 2010 · Wave OpticsLong Answer

$\text{Huygens’ principle:}$ (i) every point on a wavefront acts as a fresh source of secondary wavelets spreading out in all directions with the speed of light; (ii) the forward envelope of these wavelets gives the new wavefront at any later instant.
$\text{Single-slit diffraction:}$ a plane wavefront on a slit $AB$ of width $a$ sends secondary wavelets to a lens that focuses them on the screen. Along $\theta =0$ all wavelets arrive in phase, giving the central maximum. For direction $\theta$ the edge-to-edge path difference is $a\sin \theta$; minima occur at $a\sin \theta =n\lambda$ and secondary maxima at $a\sin \theta =(2n+1)\frac{\lambda }{2}$.
The intensity plot shows a strong central peak with much weaker side maxima (see figure).
$\text{Why secondary maxima weaken:}$ at the first secondary maximum the slit can be divided into $3$ equal strips, of which $2$ cancel in pairs and only $1/3$ contributes; at the next, $5$ strips with only $1/5$ contributing, and so on. Since a smaller and smaller fraction $\left(\frac{1}{3},\frac{1}{5},\frac{1}{7},\dots \right)$ of the wavefront is left uncancelled, the intensity of successive secondary maxima falls rapidly.