Physics · Ch 6 — Optics
Huygens' Principle
Huygens' Principle
The shape of a wavefront depends on the shape of its source and its distance from that source: a point source at a finite distance gives spherical wavefronts; an extended (line) source at a finite distance gives cylindrical wavefronts; and any source located effectively at infinity gives plane wavefronts. Huygens' principle is a geometrical construction rule for finding a wavefront's shape at a later time, given its shape at an earlier time: every point on a wavefront acts as a source of secondary wavelets, spreading outward in all directions with the wave's own speed; the common forward tangent (the envelope) of all these secondary wavelets, after elapsed time (when each wavelet has grown to radius ), gives the new wavefront's position and shape. This construction correctly reproduces a spherical wavefront expanding from a nearby point source, and a plane wavefront propagating from a source effectively at infinity. Its one acknowledged shortcoming is that it does not, by itself, explain why there is no backward-travelling wavelet ('backwave') -- an abse …
What this figure shows. Three source types are compared. A point source at a finite distance sends out spherical wavefronts, expanding as concentric circles (in cross-section) about the source. A line (extended) source at a finite distance sends out cylindrical wavefronts. Any source located effectively at infinity -- or a small piece of a very large spherical wavefront, far from its own source -- sends out wavefronts that are, to a very good approximation, flat: plane wavefronts, the case used throughout the Fraunhofer-diffract …
What this figure shows. Panel (a) shows a wavefront AB at time t=0 near a point source; every point on it (labelled P, Q, R, ...) is treated as the centre of its own secondary spherical wavelet of radius ct after a further time t, and the common forward tangent to all these expanding wavelets traces out the new wavefront A'B', itself spherical, a little further out. Panel (b) repeats the identical construction for a wavefront from a source at a very large distance, where the same tangent-envelope construction now traces out a new wavefront …