I have seen the following illustration online and had a brief lecture about Huygens principle. As far as I understood, it suggests that every point in a wavelet acts like a point source to wavelets, which explains many phenomena.

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However how do we treat the recursion here? If this is a general rule, after the infinitesimal time has passed, the generated wavelets should also behave like point sources and so on. Is this actually the case? And do we have a nice approach to it? Or are we just saying Huygens principle applies some times (when light changes medium or does interference pattern) and we do not comment this principle the other times? In other words, is this a sort of physical law that happens every instant, or a trick that holds from time to time and makes it easier to calculate?

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    $\begingroup$ It does not make a difference for the case of free wave propagation. As you can see, if you apply the principle to a spherical wave, you get the same spherical wave. For practical calculations of slits and gratings one has to use it wherever the wave interacts with a material surface. One would have to do the same for problems with random scatterers, e.g. rain, fog, ice particles etc.. $\endgroup$
    – CuriousOne
    Jan 5 '16 at 18:19
  • $\begingroup$ Why do we need concepts like waves, wavelets, or waves on waves of an infinite recursion to explain light when it can easily be explained with single photons in a particle theory alone? $\endgroup$ Jan 5 '16 at 19:00
  • $\begingroup$ If light behind an slit spread out in a spherical way the intensity distribution behind the slit has to be seen in a circle around the slit. This is the case for water waves but not for light. $\endgroup$ Jan 5 '16 at 19:16

It is actually applicable at every instant in time - but if you have a plane wave, this construction will just result in a plane wave at the next instant; and a spherical wave will continue to be spherical (just getting bigger). It's only really interesting when "something" in the path changes - refractive index, slits, etc; but it works at every point in the path, not just at discontinuities.

  • $\begingroup$ I see, then I have a follow up question: does this happen in a particular direction, or is it symmetrical? I cannot grasp this concept completely because there are so many complexities derived from it, when I consider it at every instant. For example it is really hard to imagine a plane wave is moving to + or - direction when it is symmetric. $\endgroup$
    – ozgeneral
    Jan 5 '16 at 18:38
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    $\begingroup$ You might find this answer instructive - but perhaps hard to follow. There's also this one; for further reading, see this $\endgroup$
    – Floris
    Jan 5 '16 at 18:42
  • $\begingroup$ Also see researchgate.net/publication/316994209 for a geometric derivation. $\endgroup$
    – user45664
    May 19 '17 at 23:35

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