Wavefront and Huygens' principle
A wavefront is a surface of points vibrating in the same phase. Huygens' principle builds the next wavefront from secondary wavelets sent out by every point.
What a wavefront is
Drop a stone in a still pond and circular ripples spread out. Every point on one ripple moves up and down together, in step. Light behaves the same way. Think of a point source of light in a uniform medium. After time t, the disturbance has reached every point at distance vt, where v is the speed of light in that medium. All these points lie on a sphere and vibrate in the same phase. Such a surface of constant phase is called a wavefront. The wavefront moves outward at the speed of the wave. The energy travels perpendicular to the wavefront, and a line drawn in this direction is a ray. Christiaan Huygens put forward this wave model of light in 1678.
Types of wavefront
| Source | Shape of wavefront | Rays | Example |
|---|---|---|---|
| Point source close by | Spherical (diverging) | Spread out radially | Light from a small LED bulb nearby |
| Line source (extra reading, not in your textbook) | Cylindrical | Spread out at right angles to the line | Light from a narrow lit slit |
| Source very far away | Plane | Parallel to each other | Sunlight reaching the Earth |
| Light after a convex lens | Spherical (converging) | Meet at one point, the focus | Sunlight focused by a magnifying glass |
Huygens' principle and construction
Huygens' principle tells us how to find the position of a wavefront a short time later.
- 1Every point on a given wavefront acts as a fresh source of secondary wavelets.
- 2These wavelets spread out in all directions with the speed of the wave in that medium.
- 3After a time τ, each wavelet is a small sphere of radius vτ.
- 4★Draw the common tangent (forward envelope) to all the wavelets. This surface is the new wavefront at time τ.
- 5Huygens assumed that the wavelets have zero amplitude in the backward direction, so no backward wavefront forms. A fuller wave theory later justified this.
★ key step
How to draw Huygens' construction for a plane wavefront
- Draw the first wavefront as a straight vertical line; label it F₁.
- Mark four or five points on it, such as A, B, C and D.
- With each point as centre, draw a small semicircle of the same radius vτ on the forward side.
- Draw a straight line touching the front of all the semicircles; label it F₂, new wavefront.
- Draw arrows at right angles to F₁ and F₂; label them rays.
- Write vτ along one radius. For a spherical wavefront, draw F₁ and F₂ as arcs with the same centre.
Ray vs wavefront
The two are always at 90° to each other.
Ripples spreading from a stone dropped into a temple tank are wavefronts you can see. Sunlight comes from so far away that its wavefronts reach your terrace as nearly plane waves with parallel rays.
1 marks: “What is the shape of the wavefront of light from a distant star when it reaches the Earth?” Plane, because the source is very far away and the rays are parallel.
2 marks: “State Huygens' principle.” Every point on a wavefront is a source of secondary wavelets that spread with the speed of the wave. The forward envelope (common tangent) of these wavelets after a time t gives the new wavefront.
2 marks: “Define a wavefront. Draw the wavefronts and rays for (a) a point source close by, (b) a source at a very large distance.” Locus of points vibrating in the same phase. (a) Concentric circles (spheres) with rays going out radially. (b) Parallel straight lines with parallel rays at right angles to them.
Wavefront = same-phase front. Each point sends baby wavelets; touch them all in front, and you get the new front.