# Huygens's construction

From AMS Glossary

## Huygens's construction

(Also Huygens's principle.) An approximate geometrical procedure for determining the propagation of electromagnetic (and other) waves.

According to this construction, every point of a wave front in a medium at any instant is the source of secondary spherical wavelets propagating with the phase velocity of the medium. The envelope of all these wavelets then determines the wave front at a later instant. This construction is approximate if for no other reason than that often the complicated electromagnetic fields in matter are not simple waves with well-defined fronts. Moreover, the Huygens construction in its original form requires an ad hoc obliquity factor in order to obliterate that part of the complete envelope that is not observed. This construction deflects attention from physical explanations of the propagation of electromagnetic waves: Only (charged) matter is the source of such waves, not wave fronts. Huygens's construction is sometimes useful in obtaining approximate mathematical solutions to some problems in wave propagation, but for many problems (e.g., scattering of a plane electromagnetic wave by an arbitrary sphere) this construction is useless.