Wave OpticsHuygens Principle
Drop a pebble into a still pond and rings spread out from where it fell. Every point of the surface starts bobbing up and down, and a photograph would show circles on which the disturbance is largest. All the points on one such circle are the same distance from the source, so they move in step: they are in the same phase. A surface on which every point oscillates in the same phase is called a wavefront. The speed at which a wavefront moves outwards is the speed of the wave, and the energy of the wave travels at right angles to the wavefront.
A point source that sends waves out equally in all directions makes spherical wavefronts, Fig. 10.1(a). Far from the source, the small piece of a sphere that we look at is very nearly flat: a plane wavefront, Fig. 10.1(b).
See it for yourself: the figure shows 1.8 m of a wavefront from a source R metres away.
Distance of the source R =
Up close, the wavefront curves strongly and the rays fan out from O. Far away it is flat and the rays are parallel. Light from the Sun or a distant star arrives as plane wavefronts: the Earth intercepts only a tiny patch of an enormous sphere.
Every Point a New Source
Suppose we know the shape of a wavefront at one instant, t = 0. Where will it be a moment later? Huygens answered with a geometrical construction:
Huygens principle: every point of a wavefront is a source of secondary wavelets, which spread out in all directions with the speed of the wave. The wavefront at a later time t is the forward envelope (the common tangent) of all these wavelets, each of radius vt, where v is the speed of the wave in the medium.
In Fig. 10.2, F1F2 is part of a spherical wavefront with centre O at t = 0; Fig. 10.3 does the same for a plane wavefront. Build both, then look behind them.
The wavelets from the old wavefront F1F2 all touch one surface in front of it, the new wavefront G1G2: again a sphere centred on O for the spherical wave, again a plane for the plane wave. The rays stay at right angles to both wavefronts.
The construction has one flaw. The wavelets also share a common tangent behind the old wavefront, D1D2, which would be a wave running back towards the source. No such backwave exists. Huygens simply assumed that each wavelet is strongest straight ahead and has zero amplitude straight back. That assumption was made just to get the right answer; the real reason there is no backwave comes from a more rigorous wave theory.
Note
Christiaan Huygens (1629–1695), Dutch physicist, astronomer and mathematician, founded the wave theory of light. His Treatise on Light explained the double refraction of the mineral calcite as well as reflection and refraction. He was the first to analyse circular and simple harmonic motion, designed and built improved clocks and telescopes, and discovered the true shape of Saturn's rings.
Speed Round: Wavefronts
A wavefront is a surface of constant phase, and rays are at right angles to it. A point source gives spheres; far from any source a wavefront is plane. Get five right to move on.