7 · Huygens Principle — Theory + 1 Solved PYQ (×3)

Wavefront types, three Huygens rules, refraction and reflection proofs. Easy theory then solved question.

This page covers wavefronts and Huygens’ construction. It has three short theory sections, two figures, and one solved PYQ (asked three times).

1. Wavefront: definition + three types

Freeze a wave and mark all points swinging exactly together (same phase). The surface joining them is the wavefront. Light is an EM wave (from Maxwell), so it has wavefronts.

A wavefront is a surface of constant phase, always perpendicular to the rays.

Three types

Spherical — point source nearby. Ripples on a pond after a stone drop; rays point outward radially.
Plane — source very far (sunlight). Parallel rays, flat fronts. A small piece of a big sphere looks flat (curvature $\approx 1/R \to 0$ as $R \to \infty$).
Cylindrical — line source (long slit). Tube-shaped fronts spreading sideways.

Huygens secondary wavelets spreading from points on a wavefront

Fig 1. Each point of a wavefront re-radiates; the forward envelope is the next front.

2. Huygens principle: three rules

A construction rule that builds tomorrow’s wavefront from today’s one, using small imaginary ripples.

The three rules:

Every point on a wavefront acts as a fresh source of secondary wavelets spreading at the wave speed $v$.
The forward tangent surface (envelope) of these wavelets after time $t$ is the new wavefront.
Wavelet amplitude is maximum forward and falls to zero backward (added by Stokes; explains why light goes forward only).

What it explains: reflection, refraction (Snell law, Section 3), interference, diffraction, polarization direction — qualitatively.

Note. Rule (3) is what kills the backward wave. Always mention it.

3. Refraction proof (Snell law) + reflection sketch

Snell law from wavelet speeds: a slower medium bends the front.

Formula 1. $\dfrac{\sin i}{\sin r} = \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}$, since $v = c/n$.

Refraction proof

Plane front AB hits the boundary at angle of incidence $i$. Point A enters medium 2 first and sends a wavelet of radius $v_2 t$; point B still travels in medium 1 covering $v_1 t$ before entering. The new front is the tangent from B’s position to A’s wavelet (Huygens envelope). From the two right triangles sharing the boundary intercept $L$: $\sin i = v_1 t/L$ and $\sin r = v_2 t/L$. Divide ($t$ and $L$ cancel) to get $\sin i/\sin r = v_1/v_2 = n_2/n_1$.

Reflection sketch

Same construction with one medium: incident front AB, A reflects first with wavelet $vt$, B covers $vt$ along the surface. Triangles are congruent (same speed $v$ both sides), so angle of incidence = angle of reflection.

$Huygens refraction construction with incident front, refracted front, angles i and r, speeds v1 and v2$

Fig 2. Eq. 1 drawn — incident front spans $v_1 t$, refracted wavelet spans $v_2 t$; shared intercept $L$ gives $\sin i/\sin r = v_1/v_2$.

Solved PYQ

S7-Q1

State (and explain) Huygens' principle. (2024 couples it with "dual character of light" — that half is NOT in your syllabus)

201920222024×3 Recall

A wavefront is the surface of constant phase. Huygens' construction has three rules: every point is a secondary source, the forward envelope is the new wavefront, and backward amplitude is zero (Stokes).

Steps

Define wavefront + give one type (e.g. spherical for a point source) (reason: sets up what the rules act on).
State rule 1: every point on the wavefront is a fresh source of secondary wavelets at speed $v$ (reason: needed to build the new front).
State rule 2: the forward envelope of these wavelets after time $t$ is the new wavefront (reason: defines where the wave is at the next instant).
State rule 3: amplitude is maximum forward, zero backward (Stokes) (reason: kills the back-wave that geometry would otherwise allow).
Draw secondary wavelets + forward envelope (reason: the question asks to "explain").
One use: derive Snell law $n_1\sin i = n_2\sin r$ from wavelet speeds $v_1$, $v_2$ (reason: shows you can apply the principle).

Answer

Wavefront = surface of constant phase. Rules: (i) every point is a secondary source, (ii) forward envelope is the new wavefront, (iii) no backward amplitude (Stokes). Use: Snell law $n_1\sin i = n_2\sin r$ from the envelope construction. $\boxed{\text{3 rules + envelope diagram} + n_1\sin i = n_2\sin r}$.

Exam tip

Asked ×3. In 2024 the paper couples it with "dual character of light" — that half is out of syllabus. Answer only the Huygens part and add one line "wave side is in syllabus, particle side is not".

Reference. Brij Lal, Subrahmanyam & Avadhanulu — A Textbook of Optics Ch-12; Ajoy Ghatak Ch-2 (wavefronts).