Does Huygens principle depend on the ratio of the wavelength and the dimension of the aperture? Do waves extinguish themselves by ratio 10 or more due to interference, e.g. will the wave pass through a small aperture according to Huygens principle? I think Huygens does not depend on the wavelength $\lambda$ (even if the aperture is point it emanates waves behind the slit) but there are opinions that of the $\lambda/d \gg 1$ then the wave does not pass and returns back. What is true?
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$\begingroup$ Huygens (1600s) didn't propose the "interference" it was Fresnel (1800s) and he called it the Huygen-Fresnel principle. Of note: for water waves with a single slit there is no "interference" observed! ..... Interference gains it fame from light where in both the single and double slit experiments interference is seen. But to better understand "interference" you would start with Dirac and Feynman principles .... every photon takes its own path .... and use the Feynman "path integral" to calculate the bright bands (all photons) and dark bands (no photons). $\endgroup$– PhysicsDaveCommented May 9, 2022 at 17:16
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$\begingroup$ @PhysicsDave In the end does Huygens principle allow waves to go tru if d/l is great or not? Is it valid or not? Are Feynman path integral something different from Huygence or just a math reformulation? $\endgroup$– MercuryCommented May 9, 2022 at 20:33
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$\begingroup$ Material waves like water and air will go thru much much smaller slits than the wavelength. (particle size is atom size). Light waves are very different, and as the slits get very small the EM photon wave size/extent begins to interact will the slit materials/electron/EM field (on a probabilistic basis (QM). We get diffraction, but we also see another characteristic of light .... it wants to travel paths integer multiples of its wavelength .... i.e. it wants to travel certain paths .... thus we see the "interference". $\endgroup$– PhysicsDaveCommented May 9, 2022 at 21:15
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$\begingroup$ Fresnel (1800s) explained interference by "arbitrarily" breaking the wavefront into multiple sources, it worked mathematically. But the quantum physicists of the 1900s (Einstein, Dirac, Feynman ... many more) knew that photons do NOT cancel each other (violates energy conservation) and that's why Dirac famously said "photons interfere with themselves" .... which is kind of mysterious. Feynman later clarified and said that every photons determines its own path .... and his mathematics (path integral which has been used extensively in higher QM) showed the pattern. $\endgroup$– PhysicsDaveCommented May 9, 2022 at 21:23
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$\begingroup$ @PhysicsDave In fact my question relates to the probability waves. B.e. can electron of wavelength 100 times the slit pass tru? $\endgroup$– MercuryCommented May 10, 2022 at 20:13
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I think Huygens does depend on the wavelength. Specifically, there is 1/lambda prefacror
