# Huygens' Principle of Diffraction

Huygen's principle of wave analysis helps you understand the movements of waves around objects. The behavior of waves can sometimes be counterintuitive. It's easy to think about waves as if they just move in a straight line, but we have good evidence that this is often simply not true.

For example, if someone shouts, the sound spreads out in all directions from that person. But if they're in a kitchen with only one door and they shout, the wave heading toward the door into the dining room goes through that door, but the rest of the sound hits the wall. If the dining room is L-shaped, and someone is in a living room that is around a corner and through another door, they will still hear the shout. If the sound were moving in a straight line from the person who shouted, this would be impossible because there'd be no way for the sound to move around the corner.

This question was tackled by Christiaan Huygens (1629-1695), a man who was also known for the creation of some of the first mechanical clocks and his work in this area had an influence on Sir Isaac Newton as he developed his particle theory of light.

## Huygens' Principle Definition

The Huygens' principle of wave analysis basically states that:

Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves.

What this means is that when you have a wave, you can view the "edge" of the wave as actually creating a series of circular waves. These waves combine together in most cases to just continue the propagation, but in some cases, there are significant observable effects. The wavefront can be viewed as the line tangent to all of these circular waves.

These results can be obtained separately from Maxwell's equations, though Huygens' principle (which came first) is a useful model and is often convenient for calculations of wave phenomena. It is intriguing that Huygens' work preceded that of James Clerk Maxwell by about two centuries, and yet seemed to anticipate it, without the solid theoretical basis that Maxwell provided. Ampere's law and Faraday's law predict that every point in an electromagnetic wave acts as a source of the continuing wave, which is perfectly in line with Huygens' analysis.

## Huygens' Principle and Diffraction

When light goes through an aperture (an opening within a barrier), every point of the light wave within the aperture can be viewed as creating a circular wave that propagates outward from the aperture.

The aperture, therefore, is treated as creating a new wave source, which propagates in the form of a circular wavefront. The center of the wavefront has greater intensity, with a fading of intensity as the edges are approached. It explains the diffraction observed, and why the light through an aperture does not create a perfect image of the aperture on a screen. The edges "spread out" based on this principle.

An example of this principle at work is common in everyday life. If someone is in another room and calls towards you, the sound seems to be coming from the doorway (unless you have very thin walls).

## Huygens' Principle and Reflection/Refraction

The laws of reflection and refraction can both be derived from Huygens' principle. Points along the wavefront are treated as sources along the surface of the refractive medium, at which point the overall wave bends based upon the new medium.

The effect of both reflection and refraction is to change the direction of the independent waves that are emitted by the point sources. The results of the rigorous calculations are identical to what is obtained from Newton's geometric optics (such as Snell's law of refraction), which was derived under a particle principle of light—although Newton's method is less elegant in its explanation of diffraction.

Edited by Anne Marie Helmenstine, Ph.D.

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