Is Huygens' principle true or is it a geometrical construction to figure out path of light wave? And how does it explain diffraction? I am asking in reference to physical optics. What I want to know is whether each point does behave like a light source?
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4$\begingroup$ What do you mean by "true"? $\endgroup$– Emilio PisantyCommented Sep 3, 2018 at 17:02
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$\begingroup$ see researchgate.net/publication/… $\endgroup$– user45664Commented Sep 3, 2018 at 20:24
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$\begingroup$ A physical phenomenon may have different mathematical interpretations. If they produce the same correct result, then they are all "true", even if they are very different from each other. The The Huygens-Fresnel principle does produce a correct result for light. It means, if each point behaved like a light source, we still would see exactly the same. So, does each point act as a light source? According to Huygens, yes; according to Maxwell, no. It doesn't matter, the result is the same anyway. $\endgroup$– safesphereCommented Sep 4, 2018 at 7:47
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$\begingroup$ You might find it informative to read two Wikipedia articles en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle and en.wikipedia.org/wiki/Kirchhoff%27s_diffraction_formula in which it is explained that mathematical solutions to the wave equation with appropriate approximations enables one to predict the paths of waves in a medium. $\endgroup$– FarcherCommented Sep 11, 2018 at 8:41
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$\begingroup$ No. One can not calculate a light field correctly with Huygens. On can make qualitative arguments with it, so sometimes it is "good enough". $\endgroup$– FlatterMannCommented Oct 15, 2022 at 9:27
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3 Answers
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Huygens principle (1700s) was a very good at explaining waves and interference for light and water. Using the principle a very good classical mathematical model was developed and explained the 1 or 2 slit diffraction pattern of light. However it did have some problems and to truly explain the diffraction pattern (to the best of our knowledge) the concept of a wave function was developed in the 1900s to explain the photon path. Huygens principle which relies on interference and cancellation could not explain the results of single photon experiments (no interference possible but the pattern eventually emerges) for example.
answered Sep 3, 2018 at 16:58
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$\begingroup$ Huygens did not refer to interference or its equivalent. See gutenberg.org/files/14725/14725-h/14725-h.htm $\endgroup$ Commented Sep 3, 2018 at 17:56
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$\begingroup$ "Huygens principle [...] could not explain the results of single photon experiments" - This is incorrect for two reasons. (1) The Huygens-Fresnel principle is a part of classical physics. Classical physics doesn't explain quantum phenomena whether or not you use this principle. (2) The principle applies to waves, not particles. A photon travels as a wave and its behavior is indeed explained by this principle. If you detect the photon in flight as a particle, then you don't get the interference. So the Huygens-Fresnel principle holds fine for single photon experiments like the double slit. $\endgroup$ Commented Sep 4, 2018 at 7:31
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$\begingroup$ So you're saying the HF principle holds well for the single photon experiments which is a quantum phenomenon and that the HF principle is part of classical physics which doesn't explain quantum phenomena ? $\endgroup$ Commented Sep 5, 2018 at 4:56
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Actually, all mathematical/physical principles in physics are constructs designed to produce results that accurately predict the results we find through experiments and observations. The "truth" of a physical principle isn't a proper question. Rather, the accuracy of match between its predictions and experimental results, and its consistence with other accepted principles are the main parameters that determine its usefulness and the likelihood that it will be considered an accepted principle.
Huygens' principle is a very useful predictive tool, but it is not absolutely "true". For example, the principle needs to be modified when special or general relativity and quantum mechanics are taken into account.
You also asked how Huygens' principle explains diffraction. There are many, many online answers to that question. Just do a search for Huygens and diffraction.
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$\begingroup$ Do you have any modern examples where the Huygens' principle is used? $\endgroup$ Commented Sep 5, 2018 at 4:59
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1$\begingroup$ Don't know if it counts as a modern example, but I use Huygens principle every time I teach anyone about diffraction and holography. $\endgroup$ Commented Sep 5, 2018 at 8:39
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If a field is subject to a spatiotemporal constraint — such as the wave equation or Maxwell's equations — then what happens at one point at one time influences what happens at another point at a later time. Thus there is a sense in which the first point acts as a source. The challenge is to express the "constraint" in such a way as to make the "sense" explicit.
P.S. (8 February 2020): One "sense" is that the secondary sources, by themselves, give the same wave function in a specified region as the primary sources by themselves. I have tried to demonstrate this from the most elementary possible premises: "Consistent derivation of Kirchhoff's integral theorem and diffraction formula and the Maggi-Rubinowicz transformation using high-school math".
P.S. (15 October 2022): The above link has been updated.
