Huygens principal says that every point wavefront is the source of a secondary wavelet. If this is true, why do those wavelets not interfere with the main wave? Shouldn't waves looks like a circle of interfering circles?
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$\begingroup$ of course it interferes, this is why we have diffraction $\endgroup$– hyportnexCommented Feb 5, 2017 at 2:25
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$\begingroup$ They do - but the right question is why do waves then look the way they do - with straight wavefronts. Try actually applying the pricinple and see what the interference pattern is a straight wavefront $\endgroup$– JMLCarterCommented Feb 5, 2017 at 11:22
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$\begingroup$ But why don't waves looks like this? physicsmynd.com/wp-content/uploads/2010/11/… If I look at a wave, I just see a bunch of consecutive wavefronts inside each other, not a bunch of smaller waves intersecting. $\endgroup$– N.D.H.Commented Feb 5, 2017 at 20:12
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$\begingroup$ Huygens' focused on isolated impulse-like waves and wavelets. There is only one wave front associated with each wave. So there would not be consecutive wave fronts inside each other, as you might see in sinusoidal waves. $\endgroup$– user45664Commented Feb 8, 2017 at 2:47
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$\begingroup$ researchgate.net/publication/340085346 $\endgroup$– user45664Commented Mar 22, 2020 at 18:20
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3 Answers
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Huygens' model of wave propagation breaks the 'main wave' down into its constituent points. Each of these points becomes a center for a Huygens' wavelet. At that point in the model the 'main wave' is essentially replaced by the set of wavelets--so the wavelets don't actually coexist with the 'main wave', so no interference can occur between the 'main wave' and the 'secondary wavelets'. {So this is the answer to your question.}
Then the wavelets expand equally, having equal radii, and according to him have no effect except along their common tangent in the forward direction. This common tangent then becomes the new 'main wave'. The process can be repeated to continue to propagate the wave.
The two primary problems with Huygens' Principle are:
1) the wake-- how do the wavelets have no effect except along their common tangent in the forward direction?
2) the backward wave--why is there not a second wave created along the common tangent in the backward direction?
primary references on Huygens' Principle:
"Treatise on Light" Christiaan Huygens
"The Mathematical theory of Huygens' Principle" Baker and Copson
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1$\begingroup$ see researchgate.net/publication/316994209 $\endgroup$ Commented May 19, 2017 at 22:00
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1$\begingroup$ Perhaps the italicized statement would be better expressed in terms of sources rather than waves. The secondary sources are sources which, by themselves, would generate the same downstream wave function that the primary source generates by itself. By that definition, the resultant of all the secondary waves is meant to be compared with the primary wave, not added to it. But of course the secondary waves are meant to be added to each other; that's how we explain, e.g., diffraction. $\endgroup$ Commented Jan 21, 2020 at 1:41
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$\begingroup$ Good comment--the 'main wave' becomes the new source for the next Huygens iteration. $\endgroup$ Commented Jan 21, 2020 at 17:09
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$\begingroup$ P.S.: Here's my (updated) attempt to address the above issues from first principles: "Consistent derivation of Kirchhoff's integral theorem and diffraction formula and the Maggi-Rubinowicz transformation using high-school math". $\endgroup$ Commented Oct 15, 2022 at 9:38
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Huygens principle is taught at the high school level because it was an important historical concept that broke down the old particle only theory of light and showed that a wave model would explain the observed interference pattern. It worked well until in the early to mid 1900s quantum concepts about light as a wave function more fully explained the pattern, not as interference but as viable pathways or modes for the wave function which are limited through a slit. In the modern understanding there is no interference.
An advanced understanding is really that a photon is a wave function, and a wave function is a predetermined path for the photon to take , I believe it requires a starting electron and a finishing point also an electron. Photons never superimpose but for example the electron in the nerve cell in the eye will not see 2 photons if they are out of phase with each other (180 deg), these photon will get absorbed as heat in deeper tissues.
answered Feb 8, 2017 at 4:06
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$\begingroup$ If 2 photons have exact same frequency and position (and direction), doesn't that mean that they will react the same in every point in time. That means that those 2 photons will always appear as no photons at all and will never interact with the matter? $\endgroup$– MaDrungCommented Jan 25, 2018 at 7:01
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I suggest you find a good source, and sit down and draw the wavelets out to understand it visually. As user45664 pointed out, thinking about the "main wave" is a bit misleading. Because, in this picture that you posted, you need to account for Huygen's Principle:
"...Every point on a propagating wavefront serves as the source ... of [another] wavefront..."
Namely, at the right of the circles, you gotta draw more circles for each point on each circle And then more circles on top of the new circles!! Huygen's says that all these circles will constructively and deconstructively combine to form a radiating plane-wave "trough" corresponding to the oscillatory nature of $\vec{E}$ and $\vec{B}$.
$ \ \ \ \ \ $ As an aside:
Huygen's Principle "... naturally has several shortcomings, one of which is that it doesn't overtly incorporate the concept of interference and perforce cannot deal with lateral scattering. Moreover, the idea that the secondary wavelets propagate at a speed determined by the medium ... is a happy guess." - Optics 4th edition, Eugene Hecht