Every wavefront point spawns secondary wavelets
Huygens' Principle states that each point on a propagating wavefront acts as a source of new elementary waves (wavelets). The next wavefront is formed by the envelope of all these secondary wavelets spreading outward. This principle, stated in 1678, provided an intuitive geometric picture of how waves propagate and how they diffract and refract. Consider a plane wave hitting a barrier with a slit. Inside the slit, every point becomes a source of secondary wavelets, which spread out hemispherically. The overlapping wavelets form a new wavefront on the far side of the barrier, but with a curved shape that appears to diverge from the slit (diffraction). This explains why sound bends around corners: the edges of the corner act as secondary sources.
Modern interpretation and limitations
Huygens' Principle is a classical construct that works well for macroscopic waves. Quantum mechanically, it is reinterpreted through the path integral formulation: the amplitude at any point is a sum over all possible paths the wave could take from source to that point, weighted by oscillatory factors. Modern diffraction theory uses Huygens-Fresnel diffraction integrals to compute wavefronts exactly. The principle fails to fully explain backward-traveling waves and requires supplementary arguments (e.g., only consider the expanding envelope, not the inward-moving wavelet from the back side). Despite its limitations, Huygens' Principle remains a powerful tool for understanding wave behavior intuitively and predicting qualitative effects like diffraction patterns and shadow boundaries.