Huygens's principle

Huygens's principle states that every point on a propagating wavefront acts as a source of secondary spherical wavelets, and the new wavefront at a later instant is the envelope of all those secondary wavelets. Christiaan Huygens proposed this in his Traité de la lumière (1678) as part of his wave theory of light, using it to derive reflection, refraction, and the shape of a spherical-wave wavefront around a point source. As formulated by Huygens, the principle was heuristic; it correctly predicted wavefront shapes but could not explain why wavelets appeared to propagate forward but not backward.

Fresnel repaired the theory in the 1810s–20s by adding an obliquity factor (1 + cos χ)/2 that suppresses backward-going wavelets, producing the Huygens–Fresnel principle that correctly predicts diffraction patterns quantitatively. Gustav Kirchhoff in 1883 gave the full mathematical justification via the Kirchhoff integral theorem, deriving the Huygens–Fresnel formula directly from Maxwell's equations as a consequence of Green's theorem applied to the scalar wave equation. The modern view is that Huygens's principle is a restatement of the linearity of the wave equation: a source distribution (including an aperture wavefront treated as a source) determines a field everywhere via a Green's-function integral, which is exactly the Huygens–Fresnel–Kirchhoff construction. Every diffraction-pattern calculation — Fresnel zones, Fraunhofer diffraction, ray propagation in inhomogeneous media — uses some form of this principle.