Huygens' principle


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Huygens' principle

An assumption regarding the behavior of light waves, originally proposed by C. Huygens in the seventeenth century to explain the fact that light travels in straight lines and casts sharp shadows. Large-scale waves, such as sound waves or water waves, bend appreciably into the shadow. The special behavior of light may be explained by Huygens' principle, which states that “each point on a wavefront may be regarded as a source of secondary waves, and the position of the wavefront at a later time is determined by the envelope of these secondary waves at that time.’’ Thus a wave WW originating at S is shown in the illustration at the instant it passes through an aperture. If a large number of circular secondary waves, originating at various points on WW, are drawn with the radius r representing the distance the wave would travel in time t, the envelope of these secondary waves is the heavily drawn circular arc WW. This represents the wave after t. If, as Huygens' principle requires, the disturbance is confined to the envelope, it will be 0 outside the limits indicated by points W.

Huygens' principle: the construction for a spherical waveenlarge picture
Huygens' principle: the construction for a spherical wave

Careful observation shows that there is a small amount of light beyond these points, decreasing rapidly with distance into the geometrical shadow. This is called diffraction. See Diffraction

Huygens' principle

[′hī·gənz ‚prin·sə·pəl]
(optics)
The principle that each point on a light wavefront may be regarded as a source of secondary waves, the envelope of these secondary waves determining the position of the wavefront at a later time.
References in periodicals archive ?
Given that Huygens' principle in its modern form, presents as a highly potent and successful representation of electromagnetic propagation, yet equally presents as both nonlocal and non-separable, such a depiction may then be thought to recommend itself as the model of choice for a possible reformulation of the special relativity theory in a post-EPR context.
76) In modern optics, the formal statement of the "Ewald-Oseen Extinction Theorem" is recognized as a special case of a "rigorous formulation of Huygens' principle," (77) and although not apparently recognised at the time by either researcher, is now readily apparent as a specific application of the memoryless Markov property for a wave-front mode of propagation.
Copson, The Mathematical Theory of Huygens' Principle, third ed.
This is the equivalent of Huygens' Principle in optics, where light waves are assumed to propagate with the local velocity at the wave front.
The shape of the spherulite at the next time step is then determined using Huygens' Principle of growth of a front normal to itself with an instantaneous velocity determined by the local environment as follows: At each point, n, on the interface, a new coordinate system (denoted by [prime]) is defined with the following point, n + 1, as the origin and the x[prime]-axis as the line passing through the preceding point, n - 1.