PiMath.de Planetary Systems of the Earth 1
Classic Systems
  Copyright © Klaus Piontzik  
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2.3 - Huygens-Fresnel principle

According to chapter 2.1 a ball has three degrees of freedom f = 3. Two degrees of freedom could be covered through the use of spherical harmonics
The third freedom, the radial direction, is still missing. This requires the under-standing of a physical representation with which the expansion of physical waves can be described: the Huygens-Fresnel principle.

The huygensche principle emanates from a source S, which generate wave fronts uniformly in all directions. To get the resulting wave front in the point P, it is not necessary to consider the entire spread of S.
The Huygens-Fresnel principle says that every point (O) from a wavefront can be considered as a starting point of a new wave, the so-called elementary wave.
The location of the resulting wavefront in P arises from superposition of all elementary waves.

Huygens-Fresnel principle

Illustration 2.3.1 – Huygens-Fresnel principle


The origins of the waves (O) deliver the resulting wave front (P) by superposition of elementary waves.

In two dimensions, elementary waves are circular.
In three dimensions, elementary waves are spherical in shape.


wave origins Application of the Huygens-Fresnel principle for a standing wave around a globe:

Extreme values of the wave
= sources
= waves origins

1 wave = 2 sources
Illustration 2.3.2 – wave origins  


The following image shows the oscillation state for a wave by the Huygens-Fresnel principle with a maximum (wave peak) as a source.


elementary waves
Illustration 2.3.3 – elementary waves


Since a wave consists of maxima and minima, the elementary waves also form minimal fronts (blue) and maximum fronts (red). Between the extreme fronts course zero fronts exist.

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 Planetare Systeme 1

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Der Autor - Klaus Piontzik