Huygens' principle and wavefronts
A wavefront is a surface of points vibrating in the same phase. Huygens' principle builds each new wavefront from secondary wavelets sent out by every point.
What a wavefront is
Drop a stone into still water in a wide trough. Circular ripples spread out, and every point on one ripple moves up and down together, in the same phase. The line joining such points is a wavefront: the locus of points vibrating in the same phase. A point source of light in a uniform medium sends out spherical wavefronts; a line source, such as a narrow lit slit, sends out cylindrical ones. Far from the source, a small part of a wavefront is nearly flat: a plane wavefront. A line drawn at right angles to the wavefront shows the direction in which it moves. This line is a ray, and a bundle of rays is a beam. Christiaan Huygens, who lived at the time of Newton, proposed that light is a wave. He imagined it travelling through an invisible medium called ether; later work showed that light needs no medium at all.
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 | 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.
- 5The wavelets travel only forward: no backward wavefront forms. In a uniform medium, energy spreads equally in all directions.
★ key step
How to draw Huygens' construction for plane and spherical wavefronts
- 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.
Worked example: radius of the wavelets
(a) In Huygens' construction for light in glass (μ = 1.5), what radius should the wavelets have to find the wavefront 1 ns later? (b) A point on a wavefront starts sending out wavelets at t = 0. Compare the radii of its wavelets at t = 2 ns and t = 5 ns. (c = 3 × 10⁸ m s⁻¹)
- (a) Speed in glass: v = c/μ = 3 × 10⁸ m s⁻¹ ÷ 1.5 = 2 × 10⁸ m s⁻¹.
- Radius = vt = 2 × 10⁸ m s⁻¹ × 1 × 10⁻⁹ s = 0.2 m.
- (b) The radius is vt, so it is proportional to t.
- r(2 ns) : r(5 ns) = 2 : 5.
(a) 0.2 m; (b) 2 : 5
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, which spread out with the speed of the wave. The forward envelope (common tangent) of these wavelets at a later time gives the new wavefront.
2 marks: “Define a wavefront. What is the angle between a ray and its wavefront? Name the wavefront from a line source.” The locus of all points vibrating in the same phase. The ray is at 90° to the wavefront. A line source gives a cylindrical wavefront.
Wavefront = same-phase front. Each point sends baby wavelets; touch them all in front, and you get the new front.