Huygens' Principle

Huygens sought a general rule that could take the known shape and position of a wavefront at one instant and predict its shape and position at any LATER instant, treating light as a mechanical-style wave (analogous to water or sound waves) propagating through his hypothesised ether. This rule -- Huygens' Principle -- can be stated as: 'Each point on a wavefront acts as a secondary source of light, emitting secondary spherical wavelets in all directions, travelling at the wave speed of the medium. The new wavefront, at a later instant, is obtained by taking the forward ENVELOPE (the common tangent surface) of all these secondary wavelets. Wavelets travelling in the backward direction are declared ineffective.'

Applying this construction to a plane wavefront AB at time t = 0 (Fig. 7.2(a)): every point along AB becomes a secondary source, emitting forward-travelling hemispherical wavelets (only the forward halves are drawn/considered, per the principle's backward-ineffective clause). By a later time $t = T$, each of these hemispherical wavelets has grown to radius $vT$ (v being the wave's speed in the medium). Their common forward envelope -- the new wavefront at time T -- works out to be another PLANE, A'B', parallel to the original AB and displaced forward by exactly $vT$: Huygens' construction correctly reproduces the fact that a plane wave stays plane as it propagates. Applying the identical construction to a SPHERICAL wavefront (Fig. 7.2(b)) similarly shows that the envelope of the secondary wavelets is another sphere, concentric with the original, with its radius increased by $vT$: a spherical wave stays spherical (and centred on the same point) as it propagates.

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