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Juang Dsi
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The incompleteness of Huygens principle has been discussed at length here and elsewhere, and has actually been completed, regarding wave propagation and refraction, relatively shortly afterwards (by Kirchhoff and Fresnel).
This post is specifically about reflection, and should you be familiar with the Huygens version of reflection, you may move on to b).
a) The Huygens principle offers a simple explanation of wave-front reflection, based on secondary wavelets that are exerted at each point that the wavefront passes. According to this, the traveling time of a wavelet from A to B (see Figure) equals the time of a wavelet from A' to C plus the time of a wavelet exerted at C to arrive at B'. By definition of C', CB'=C'B, and from this it follows that the two outer angles at C are equal (see Figure).
b) In this derivation, no use is ever made of the physical properties of the line DCB being a mirror, that is, of the waves not passing through DCB. If it is true, therefore, a reflection must occur at any given line/plane in space, whether being a real mirror or just an imagined one, and reflected waves must be found all over the place.
The question is now: Can Huygens reflection be rectified in any simple way - for example, by employing the angular dependence of Fresnel/Kirchhoff?
It seems the same argument and question apply to diffraction as well.
This post is specifically about reflection, and should you be familiar with the Huygens version of reflection, you may move on to b).
a) The Huygens principle offers a simple explanation of wave-front reflection, based on secondary wavelets that are exerted at each point that the wavefront passes. According to this, the traveling time of a wavelet from A to B (see Figure) equals the time of a wavelet from A' to C plus the time of a wavelet exerted at C to arrive at B'. By definition of C', CB'=C'B, and from this it follows that the two outer angles at C are equal (see Figure).
b) In this derivation, no use is ever made of the physical properties of the line DCB being a mirror, that is, of the waves not passing through DCB. If it is true, therefore, a reflection must occur at any given line/plane in space, whether being a real mirror or just an imagined one, and reflected waves must be found all over the place.
The question is now: Can Huygens reflection be rectified in any simple way - for example, by employing the angular dependence of Fresnel/Kirchhoff?
It seems the same argument and question apply to diffraction as well.
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