Is Huygens' Principle of Reflection Incomplete?

[Juang Dsi]

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.

 

[eljose79]

I agree that the incompleteness of Huygens principle in regards to reflection has been addressed by Kirchhoff and Fresnel's work on wave propagation and refraction. However, it is important to note that Huygens principle still provides a valuable conceptual framework for understanding wave behavior, and it should not be dismissed entirely.

Regarding the specific issue of reflection, it is true that Huygens principle does not explicitly consider the physical properties of a mirror. However, it does take into account the fact that waves do not pass through the surface of a mirror, as evidenced by the equal angles at C in the figure provided. This is a crucial aspect of reflection that is captured by Huygens principle.

To address the question of whether Huygens reflection can be rectified by incorporating Fresnel/Kirchhoff's work on angular dependence, it is important to understand that Huygens principle is a simplified model and does not account for all factors involved in reflection. Fresnel and Kirchhoff's work takes into account more complex factors such as the angle of incidence and the properties of the reflecting surface. Therefore, while Huygens principle may not fully explain the phenomenon of reflection, it can still provide a useful starting point for understanding the basics of wave behavior.

The same can be said for diffraction. Huygens principle does not account for all aspects of diffraction, but it does provide a simple explanation for the phenomenon. Incorporating Fresnel and Kirchhoff's work can help to refine and improve our understanding of diffraction, but it does not invalidate the usefulness of Huygens principle.

In conclusion, while Huygens principle may have limitations in explaining certain aspects of wave behavior, it still serves as a valuable tool for understanding the basics of wave propagation. Incorporating more complex factors, such as those explored by Fresnel and Kirchhoff, can help to improve our understanding and provide a more complete picture of wave phenomena.