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My understanding of Huygens' principle is, that it describes the way how a wave moves: Instead of moving straightforward, it propagates in all directions via producing secondary wavelets. 'Secondary wavelets' and 'wave's propagation' are synonyms.

But I realized that many others assume that waves move straight, and Huygens' principle doesn't say anything about the original wave, just that in addition to the original wave that moves straight, there are also secondary wavelets which are spherical. And these wavelets just continue straight, because Huygens' principle only applies to waves, not wavelets. I wonder if it could be the correct interpretation, because it seems to void most of Huygens' principle. For example, if refraction occurs due to Huygens' principle, refracted waves shouldn't be able to refract again, because they are composed of those wavelets, since the original wave just continues straight. So it's not a 'real' wave, and Huygens' principle doesn't apply to it.

Now to my main question (with my understanding of Huygens' principle): Let's start with the most simple case: propagation of waves in free space. Suppose we have a planar wavefront of troughs followed by a wavefront of crests of the same waves (½ wavelength behind). After one revolution, we have a lot of semicircular secondary wavefronts superimposed on each other all along the initial wavefront. (We should really have full spherical wavefronts, but for now let's ignore backward waves, and focus on 2 dimensions only, considering only the forward semicircles. It's enough complicated as is.) The result is a thick wavefront starting from the location where the wavefront initially was, and ending one wavelength ahead. After another revolution, we have a wavefront twice as thick. The starting point never changes (as long as we ignore backward waves), but the endpoint does, so the wavefront is just growing. The same is true for the wave crests (and everything in between), just their start and end points are a half wavelength behind. So behind the very first part of the waves - where the troughs have no crests to compete with - we should have destructive interference in every wave.

Here is how it should look after one revolution:wavefronts after 1 revolution Whatever the answer should be, one needs to be careful that only straightforward waves should survive. And I'm not concerned specifically about backward waves (and I have no idea why people assumed so), but about every possible direction.

I think that the answer may be that although there are troughs and crests all over, they have different densities, which causes that some parts should survive. But I'm waiting for others to confirm it before diving in the details.

When it comes to refraction, the problem with direction gets worse. If every point of a wavefront produces waves in every direction with and without refraction, then how can waves change direction? What exactly is different after refraction than before?

The question gets even more complicated, when we have refraction and diffraction simultaneously. In that case the side waves don't get canceled (this is the cause for diffraction), so how can refraction have an effect?

Some commenters told me that Huygens' principle is not accurate. It's just an approximation. I wonder if they're right, because I didn't see such a statement anywhere. If they're right, then I'm not interested in understanding Huygens' principle, because I'm interested in the real facts of wave propagation.

One of them told me that the exact truth is Maxwell's equations. But I couldn't find an interpretation of Maxwell's equations which predicts wave propagation, at least not a well explained one.

This is really a fundamental question. If you know of an article or inexpensive ebook etc. that explains this in a way that all my questions will be answered, please give me a link. (in addition to, or without, your answer.) (It's not easy to find. I searched a lot before posting this question.)

George Lee
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  • Are you looking for a mathematical explanation? Is calculus OK? – G. Smith Sep 22 '20 at 19:13
  • @G.Smith No. I'm looking for a layman explanation. – George Lee Sep 23 '20 at 15:14
  • @G.Smith: I see that no answer is coming, so I'm changing my mind. Even if I will not understand, it may be helpful for others. But please try to make it relatively simple, so it will be helpful for me too. (I know some very basic calculus) – George Lee Sep 24 '20 at 15:54
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    Huygens did not know anything about the wavelength of light, did not know about superposition or interference of light. He used it to explain (double) refraction. The principle is not fundamental in any way. It is not even really true. –  Oct 01 '20 at 20:49
  • @Pieter: Then how would you explain slit interference? – George Lee Oct 02 '20 at 17:56
  • @GeorgeLee Interference was discovered and explained by Thomas Young, a long time after Huygens. The explanation does not involve Huygens' principle. –  Oct 02 '20 at 18:21
  • @Pieter interesting point, although Huygens’ principle is the only theory by which I understand why shorter and bigger wavelengths diffract differently, as explained here: https://physics.stackexchange.com/a/125973/137288 –  Oct 02 '20 at 18:57
  • @Pieter: Wikipedia explains it with Huygens' principle, and I never heard a different explanation. Can you please cite a different explanation? – George Lee Oct 05 '20 at 23:46
  • @GeorgeLee Huygens was not aware of wavelengths or diffraction, so when one uses that it is more properly the Huygens-Fresnel principle (if you rely on Wikipedia https://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle ). But that was before Maxwell's explanation with electromagnetic waves. And that was before Feynman's explanation with photons (quantum electrodynamics). –  Oct 06 '20 at 09:03
  • General tip: The title or question body is not the appropriate place to write "unsatisfied with current answers". (That should be a comment to an answer.) – Qmechanic Feb 05 '21 at 16:33
  • @Qmechanic I did it because people tend not to answer if there are already existing answers. – George Lee Feb 07 '21 at 02:53
  • Well, how do the Phys.SE community know that you don't forget to update the title when you're satisfied? – Qmechanic Feb 07 '21 at 16:10
  • As long as there are no more recent answers than my last update, there's no doubt. But I promise I will update. – George Lee Feb 08 '21 at 15:08
  • The way to show that you are unsatisfied with current answers is to offer a bounty. – Javier Feb 09 '21 at 00:48
  • @Javier I would do it if I had enough reputation. – George Lee Feb 09 '21 at 15:09

3 Answers3

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Imagine a simple plane wave, moving to the right, in a direction perpendicular to the wavefronts (i.e., to the "isophase planes"). Huygens wavelets emitted at all points on a given wavefront interfere constructively with each other in the forward direction, as you know. They never interfere with the wavelets from another wavefront in the same wave train, because they are moving at the same velocity as the wave train.

You want to know why there is destructive interference in the backward direction. To reach that understanding, you need to introduce something that accounts for the fact that the wave is actually moving.

The Huygens principle as it is usually presented can easily lead to confusion. The normal presentation begins with the assumption that every wave is actually a monochromatic wave train that starts out stationary. If that were true, there would be waves moving in both the forward and backward directions.

So, now re-do Huygens principle, taking time into account. In the backward (left) direction, an emitting point on the forward moving wavefront encounters backward-moving wavelets emitted by the forward-moving wavefront to the right of it, because it has moved to the right. The encounter is slightly too soon to be in step, because of the fact that the backward-moving wavelet travels less than a full wavelength before hitting the advancing left wavefront. Add that up over all the wavelets emitted by all points in the wavefronts ahead of it, and the sum washes out to zero: that is destructive interference, so this version of Huygens principle does not produce a backward-moving wavefront.

Edited 10/1/20

S. McGrew
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    I agree that by this explanation there would be destructive interference.. but would it prevent backward waves? Because if the previous source emits a circular wave, and moments later, a source ahead emits another wave, the “previous” wave would always be “ahead” in the backward direction, since the velocities of both would be the same. Does that make sense? –  Sep 30 '20 at 16:42
  • Not quite. Please try again. But first, make some sketches and think some more. – S. McGrew Sep 30 '20 at 17:04
  • The point is that in the forward direction there is constructive interference; and in the backward direction there is destructive tnterference. – S. McGrew Sep 30 '20 at 18:30
  • I’ll try to explain myself. You are posing there are two sources slightly out of phase: one slightly ahead of the other. If they both send waves at the same velocity, at the same time.. how would the wave sent back from the “source ahead” be able to reach the entirety of the wave from the “previous source” to completely cancel it? If they are at the same velocity but one ahead of the other? –  Sep 30 '20 at 18:44
  • By the way, are you familiar with this article? https://ee.stanford.edu/~dabm/146.pdf It poses a similar explanation as yours, but slightly different about the time each source is “activated” –  Sep 30 '20 at 18:46
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    Yes, I am familiar with that article. I'm not very comfortable with the author's assignment of a dipole property to each point, though it may be mathematically equivalent. – S. McGrew Sep 30 '20 at 19:00
  • Let us continue this discussion in chat. –  Sep 30 '20 at 19:05
  • "...interfere constructively in the forward direction, as you know. You want to know..." — Yes, I know, but I don't understand - as you can see in the 4th paragraph of my question. I'm not concerned about the backward wave more than about any other wave, they all evenly don't make sense to me. – George Lee Oct 01 '20 at 16:59
  • All I can recommend is that you try drawing diagrams to test and expand your understanding. Maybe a better starting point is to make sure you properly understand the principles of interference per se. – S. McGrew Oct 01 '20 at 18:26
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    When ignoring the circular wavelets (as you - and everyone - did), and focusing only on front and back, I find that after propagating a quarter of a wavelength, there is destructive interference between the front and back waves. But after another quarter, there is constructive interference. This means that the backward wave is not canceled. – George Lee Oct 01 '20 at 18:32
  • Yes, I'm doing it (drawing diagrams) all the time. And this is where my questions come from... OK I will show you some by editing the question. (not necessarily soon) – George Lee Oct 01 '20 at 18:36
  • ... But I don't really know how it will help, because I will anyway need to explain every diagram, so I can explain it without the diagram too. (I think I did it already). How about you should post diagrams in your answer? Maybe this will help. Please assign a time to every diagram. – George Lee Oct 01 '20 at 18:49
  • I guess I don't want to put that much effort into something that seems obvious to me! However, I'll add a bit more to the explanation in my answer. – S. McGrew Oct 01 '20 at 19:02
  • "They never interfere with the wavelets from another wavefront in the same wave train, because they are moving at the same velocity as the wave train." – That's true for the very first wavefront, but the others could have interfered destructively in their way, exactly in the way you described backward waves. – George Lee Oct 02 '20 at 03:01
  • Can you please also include in your answer an explanation for where refraction and diffraction occur simultaneously? – George Lee Oct 02 '20 at 03:04
  • If you would like that answered, please ask in the form of a new question. – S. McGrew Oct 02 '20 at 03:38
  • Let us continue this discussion in chat. – George Lee Oct 02 '20 at 17:58
  • I just rewritten my question more clearly. Please take a look and contribute when you have a chance – George Lee Feb 05 '21 at 16:07
  • Sorry, didn't see the request to continue in chat. You might try labeling each advancement of the circular wavelets according to what time they arrive at the place where you have drawn them while thinking about this. You will only get constructive interference when wavelets arrive at the same point at the same moment. It's destructive if they arrive a half-cycle apart. – S. McGrew Feb 05 '21 at 16:36
  • Every wavelet in my diagram is of the same time: after one revolution. – George Lee Feb 07 '21 at 03:00
  • In that case you probably have two wavefronts in your drawing: one at t=0, and another at t=1, in units of the wave period. Try addint t=-1 and t=2, and see what overlaps with what (& where). Just trying to help you build your intuition. – S. McGrew Feb 07 '21 at 14:58
  • No. If you read my question carefully, you will see that both are at t=1, the red ones are crests and the blue ones are troughs, and the distance between them is ½ wavelength. – George Lee Feb 08 '21 at 15:13
  • Granted, that's what is in your question. I'm saying that you should, for your own benefit, try my suggestions. I think it will help you understand what's going on, and what is lacking in the usual explanations of Huygens Principle. – S. McGrew Feb 08 '21 at 15:47
  • I suspect that we have fundamental differences in understanding Huygens' principle. Please see the first part that was just added to my question. And let me know what you think about it. – George Lee Feb 09 '21 at 19:49
  • The basic problem is that, as usually (incorrectly) presented, Huygens Principle starts with a stationary distribution of energy (the wavefront), then releases it. The energy will travel in both directions just as you imagine. However, when properly presented, Huygens Principle has a direction of travel built-in. It's possible to modify the usual Huygens principle to include direction of travel if you use two wavefronts, spaced a half wavelength apart and launched at times a half period apart. – S. McGrew Feb 09 '21 at 20:48
  • It makes for a fairly complicated diagram. Both wavefronts represent the same wavefront at different times, but traveling in a given direction. The "more advanced" wavefront goes in both directions, and interferes destructively with the "less advanced" wavefront in the backwards direction, but constructively in the forward direction. – S. McGrew Feb 09 '21 at 20:49
  • Another way to look at it is that the only way to establish a stationary "wavefront" is in the form of a standing wave. Looking at that in reverse, every stationary "wavefront" is actually composed of two waves traveling in different directions. Take one of those waves away, and we have a traveling wave that was never stationary. – S. McGrew Feb 09 '21 at 20:51
  • Ok. So you understand it just as I described in the second paragraph of my question. So what would you answer to my question there about refracting twice? – George Lee Feb 10 '21 at 15:18
  • Not sure what you mean by waves moving "straight". In fact, the whole second paragraph seems really difficult to follow, since it appears you don't use "refract" as meaning what it usually means. It would probably be a good idea to move this to Chat. – S. McGrew Feb 10 '21 at 16:21
  • Here is the chat room: https://chat.stackexchange.com/rooms/119590/huygens-principle – S. McGrew Feb 10 '21 at 16:26
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The wave equation has two initial conditions: the initial displacement, and the initial speed of the initial displacement. If the initial speed of the initial displacement is given the appropriate value then the backward wave is canceled. As an ongoing wave propagates this happens 'automatically' so there are no backward waves in an ongoing wave.

See my

https://www.researchgate.net/publication/340085346

Huygens' Principle geometric derivation and elimination of the wake and backward wave, rev2, 3/21/20

especially the appendices, particularly appendix D. {sorry for the math--hope its ok}

Now there is a peer reviewed version (Nature Scientific Reports):

https://www.nature.com/articles/s41598-021-99049-7

user45664
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  • It's very technical and hard to understand. If you or anyone can explain it in a simple way, it would be very appreciated. – George Lee Sep 27 '20 at 20:48
  • I do not know of a simpler explanation--wish I did. – user45664 Sep 27 '20 at 21:15
  • @user45664 if the “initial displacement” was produced by the moving planar source you mention, while already moving with said velocity, would it also create waves only ahead of its path and not back? Or does this model only work in the context of an already propagating wave? –  Sep 30 '20 at 23:20
  • In either case, if the source is moving at the wave propagation speed, there would be no backward wave. – user45664 Oct 01 '20 at 16:56
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    Suppose a planar source is moving in some direction, and begins sending waves forward and backwards at the same speed. I’m having a hard time understanding why there wouldn’t be any wave opposite to its direction of movement. What would cancel it? –  Oct 01 '20 at 22:06
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    The wave sent backwards due to the source motion is negative, canceling the original backward wave. – user45664 Oct 02 '20 at 00:27
  • Interesting! Thanks! –  Oct 02 '20 at 00:33
  • What do you mean by 'negative'? Do you mean 'has a phase shift of a half wavelength'? – George Lee Oct 02 '20 at 02:48
  • Yes--or inverted for a pulse. – user45664 Oct 02 '20 at 03:36
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You can find an explanation by fermilab about the 'true' way light works. In his explanation, he tells that although there is constructive interference that creates correct waves in the forward direction in Huygens-Fresnel principle, it also predicts there are waves that propagates to the sides, which is invalid(unless talking about quantum probability).

Although, it doesn't explain about reflection, just about refraction, but it still gives you the correct idea about why light does these things. In his explanation about refraction, you need to understand that light is also an electromagnetic wave, and everything is a wave according to the quantum field theory, focus on the electric part, when light enters a medium, the electric wave of the light interacts with the electrons of the medium, causing the electrons to vibrate, this creates a new electric wave which combines with the light wave to create a brand new wave that is a brand new sort of quasi particle which has mass, this is why it slows down when entering a medium, since it is basically transformed into another entity. When it escapes the influence of the electrons, the wave will go back to normal and turns back into regular light.

In another video of his, he also explains the bending property of refraction in light, he said that it is also caused by the same property as to why light slows down. You see, in light, there are two waves that must be perpendicular to each other, these two waves combine into light. I have explained before that light has an electric wave which effects electrons, which in turn creates new waves that pushes back, this pushing back action, changes the electric wave's strength in one coordinate and thus, changing its overall direction, and because light must be perpendicular to it, it bends. You can test it out yourself by making the diagrams.

If you need further explanation, search the videos titled, "Why light slows down in water" and, "Why light bends in glass" by Fermilab, that's where I got my information from. I am not competent enough to figure out from this theory how 'reflection' works, maybe someone else in this post will be able to continue this brand new source.

Alvsecret
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