Wavefronts and Huygens principle

Drop a pebble into still water and circular ripples spread out. All points on one ring are the same distance from where the pebble fell, so they rise and fall together.

A wavefront is a surface joining points that vibrate in the same phase: a surface of constant phase. The speed at which a wavefront moves outward is the wave speed, and the energy of the wave flows at right angles to the wavefront.

A point source radiating equally in every direction gives spherical wavefronts. Far from the source, a small patch of such a sphere is almost flat, and the wave there is a plane wave with plane wavefronts.

Huygens principle is a geometrical rule for getting a later wavefront from an earlier one. Every point on a wavefront acts as a source of secondary wavelets, which spread in all directions at the speed of the wave.

To find the wavefront a time τ later, draw spheres of radius vτ centred on points of the present wavefront, where v is the wave speed in the medium. The common tangent to all these spheres, the forward envelope, is the new wavefront.

For a spherical wavefront centred on O the new wavefront is again a sphere centred on O. For a plane wavefront the new one is a parallel plane further on. Rays are lines drawn at right angles to the wavefronts.

The construction also yields a backward envelope, a backwave, which is never observed. Huygens removed it by assuming that the wavelets are strongest straight ahead and vanish backwards. That was an ad hoc fix; the real justification comes from a more complete wave theory.

Wavefront shapes to recognise (Exercise 10.2): light spreading from a point source has spherical wavefronts; light leaving a convex lens with a point source at its focus has plane wavefronts; the part of a distant star's wavefront that reaches the Earth is plane.