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I have an extremely basic doubt about Huygens Principle:

Every point on the wavefront may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wavefront is the tangential surface to all these secondary wavelets.

enter image description here

My doubt is about how many sources we have to consider to analyze a wave in a certain region of space. Consider a source of an electromagnetic wave (an antenna, a lamp etc). It generates and EM waves, and we may find the electric and magnetic field in each point of space, if we know the source and medium properties. In this analysis, why do not we consider that each point of wavefront is a new suorce of EM waves?

I think that maybe Huygens principle states that we do not have to consider both the original physical source and all secondary sources (points of wavefront), but only one of them. In other words, if I consider only the physical source, or only the points of a wavefront (as in the previous picture) by ignoring what happens before them (and so the physical source), the result is the same. If this interpretation I have thought is true, it may be an equivalence theorem.

But each formulation of Huygens principle I have read does not say that we should consider the physical source OR wavefront secondary sources: it simply says that wavefront points are sources. So, it may seem that we have to consider the physical source AND wavefront secondary sources.

Can you help me on understanding this better?

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  • $\begingroup$ Huygens principle is most often used when the wave from the original source has been obstructed or modified $\endgroup$
    – R.W. Bird
    May 18, 2020 at 18:21

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Every point on the wavefront may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wavefront is the tangential surface to all these secondary wavelets.

The word new is the key to your question. Huygens' Principle explains wave propagation in steps: 1) decompose to original wave front into its constituent points. 2) let each point be the source of a wavelet. 3) form the tangential surface to the wavelets in the forward direction. 4) this becomes the new wave front. 5) repeat 1) thru 4) to continue the propagation.

So your

But each formulation of Huygens principle I have read does not say that we should consider the physical source OR wavefront secondary sources: it simply says that wavefront points are sources. So, it may seem that we have to consider the physical source AND wavefront secondary sources

points out a valid problem with the typical description of Huygens' Principle: As you say "OR" should have been used.

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  • $\begingroup$ Perfect, thank you very much $\endgroup$
    – Kinka-Byo
    May 18, 2020 at 18:28

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