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As I understand the Huygens principle, all points on the wavefront are sources of secondary spherical wavelets and the tangent to these wavelets will form new wavefront. This is used to prove the laws of reflection and refraction by drawing these spherical wavelets emanating from the surface separating the 2 mediums and then constructing new wavefront, like e.g. shown here.

I don't get why this construction is valid. As I understand, in Huygens principle, we derive new wavefront from the prior wavefront. But the points on the surface (separating 2 mediums) do not seem to constitute a wavefront at all. If a wavefront is a set of points having the same phase, and the original wavefront was at an angle to the surface, it seems that the points on the surface would not be in the same phase. If they are not, then the surface does not constitute a wavefront, so we can't derive reflected or refracted wavefront from it.

What am I missing here?

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  • $\begingroup$ All points of the the heavy lines (blue segments & grey hemispheres) have the same 1 phase, although other aspects can be interpreted in various ways. $\endgroup$
    – philipxy
    Commented Jun 28 at 21:51

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The construction you link to shows the same wavefront at multiple points in time, not a snapshot of a light wave at one point in time. The yellow dots constituting the point sources at the interface of the two mediums, ultimately resulting in the refraction of the light ray, are created at four different time points all created by the same wavefront as it is incident on the interface. This is why the point sources are shown to have traveled less in the second medium,from left to right (because they are created later).

Here is a gif of Huygens' Principle to help with the visualization.

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  • $\begingroup$ Maybe I misunderstand the Huygens principle then. In this case, how can we take the yellow dots, created at different points in time, and construct spherical wavelets from them that will result in the new refracted wavefront, which represents points at the same time and in same phase, I mean the green lines of the refracted wave. If we are allowed to do that, then what makes the points on the surface special at all? We could've just as well then taken some other points in the incoming wave that have same phase but at different times. $\endgroup$
    – Yevgeniy P
    Commented Jun 29 at 11:49
  • $\begingroup$ I'm not entirely sure I get your question. However, the point is you cannot choose the yellow dots, however you please. You can only choose yellow dots where the wavefront (the blue line) intersects the interface. Think of the construction as a flip book where we draw every frame instead of flipping through them. Another point, is that just because the yellow dots are created at different times, doesn't mean that they can't overlap with the waves propagating out from yellow dots created previously. It just means that they had less time to propagate (this is in fact what causes refraction). $\endgroup$
    – hijit
    Commented Jun 29 at 12:56
  • $\begingroup$ @YevgeniyP Maybe the gif I added to the original answer, will help visualize the huygens principle $\endgroup$
    – hijit
    Commented Jun 29 at 13:04
  • $\begingroup$ Thanks for the gif. I think the backpropagating wave is the reflected wave. You said that we can only choose the yellow dots where the wavefront intersects the interface. My question is why. From the definition of the Huygens principle that I can find, it doesn't mention the interface, only the wavefront. $\endgroup$
    – Yevgeniy P
    Commented Jun 30 at 12:08
  • $\begingroup$ yeah right, that's the reflected wave. But yeah Huygen's principle states that every point on the wavefront is the source of a new point source. The yellow points can only be selected at the intersection of the interface and the wavefront because they are on the wavefront. The only reason we highlight them as yellow is because at this point light propagates out slower from these points (since we enter a new medium). That is why, if you look at the construction, the green wave lines are drawn closer together than the blue ones. $\endgroup$
    – hijit
    Commented Jun 30 at 13:12
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The points shown as yellow blobs on your diagram are in phase, even though they are not on the same wavefront. The hemispheres drawn in the lower medium do seem like Huygens secondary wavelets. But then, you ask, what about the points midway between the yellow blobs? Surely these act as sources in antiphase with the yellow blobs. Wavelets from these antiphase sources will land up in phase with the yellow blob wavelets on the same straight envelope wavefront in the lower medium. I think that the construction is alright, but it's not a straightforward application of H's principle.

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