In the formulation of Huygens principle, it is said that the secondary waves are spheres but on the plots for determination of the wavefront there suddenly become hemispheres? What is the reason for this mismatch? Is there any physical explanation based on the momentum of the incoming wave in the sense that it influences the atoms of the media? What media does one have in case of EM waves? Maybe Huygens does not have any physical meaning but is just an observational geometrical rule?
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$\begingroup$ check out inclination factor $K(\chi)$ see en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle $\endgroup$– hyportnexCommented Dec 5, 2022 at 17:40
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In the formulation of Huygens principle, it is said that the secondary waves are spheres but on the plots for determination of the wavefront there suddenly become hemispheres?
The whole sphere is often not shown as a convenience in creating the plot. Also, showing only half of the sphere avoids the issue of the backward wave.
See my https://www.nature.com/articles/s41598-021-99049-7 ("Huygens' Principle geometric derivation and elimination of the wake and backward wave") for a discussion. This paper also shows how the backward wave is eliminated when the secondary waves, the Huygens' wavelets, are whole spheres. No inclination factor is needed.
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$\begingroup$ Admiration! I try to read it but have not much time right now because of a project on wavefunction reality. If all is true in your paper it definitely must enter in textbooks on waves along Huygence!!! Can you just tell briefly the main idea? Why do backwaves not show. My opinion was that they interfere negatively with wavelets from behind. But may the forward momentum plays a role? Also I am very interested in the physical content of the case not just geometry. $\endgroup$– MercuryCommented Dec 6, 2022 at 11:24
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$\begingroup$ Re. "Can you just tell briefly the main idea? Why do backwaves not show" The main idea: A stationary point source emits both forward and backward waves. However a point source moving at the wave propagation speed emits both the previous forward and backward waves and also a forward wave and a negative amplitude backward wave which cancels the original backward wave. $\endgroup$ Commented Dec 6, 2022 at 18:12
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$\begingroup$ This can be derived either from the geometry or the math which follows from D'Alemberts solution to the 1D wave equation. Re. "Maybe Huygens does not have any physical meaning but is just an observational geometrical rule?" The geometry and the math follow directly from the physics--essentially describing the physics. $\endgroup$ Commented Dec 6, 2022 at 18:26