Talk:Huygens–Fresnel principle

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Mathematical expression of the principle

Geometric arrangement for Fresnel's calculation

Consider the case of a point source located at a point P₀ vibrating at a frequency f, where the disturbance is described by a complex variable U₀. It generates a spherical wave with wavelength λ, wavenumber k = 2π/λ. The primary wave disturbance at the point Q located at a distance r₀ from P is given by

$U(r_{0})={\frac {U_{0}e^{-ikr_{0}}}{r_{0}}}$

since the magnitude decreases in inverse proportion to the distance travelled, and the phase changes as k times the distance travelled.

Using Huygen's theory, and the principle of superposition of waves, the disturbance at a further point P is found by summing the contributions from each point on the sphere of radius r₀. In order to get agreement with experimental results, Fresnel found that the individual contributions from the secondary waves on the sphere had to be multiplied by a constant, i/λ, and by an additional inclination factor, K(χ). The first assumption means that the secondary waves oscillate at a quarter of a cycle out of phase with respect to the primary wave, and that the magnitude of the secondary waves are in a ratio of 1:λ to the primary wave. He also assumed that K(χ) had a maximum value when χ=0, and was equal to zero when χ = π/2. The disturbance at P is then given by:

$U(P)={\frac {iU(r_{0})}{\lambda }}\int _{S}{\frac {e^{-iks}}{s}}K(\chi )\,dS$

where S describes the surface of the sphere, and s is the distance between Q and P.

Fresnel used a zone construction method to find approximate values of K for the different zones, which enabled him to make predictions which were in agreement with experimental results.

The various assumptions made by Fresnel emerge automatically in Kirchhoff's diffraction formula, to which the Huygens–Fresnel principle can be considered to be an approximation. Kirchoff gives the following epxression for K(χ):

$~K(\chi )=-{\frac {i}{2\lambda }}(1+\cos \chi )$

This incorporates the quarter cycle phase shift and the reduced magnitude; K has a maximum value at χ = 0 as in the Huygens–Fresnel principle; however, K is not equal to zero at χ = π/2. Epzcaw (talk) 14:44, 23 April 2011 (UTC)

I fixed a couple of points on the version of this section that appears in the article:

• I changed the sign of the prefactor which now is −i/λ. This is consistent with the article using the convention exp(iks) instead of the exp(−iks) convention used above.
• I removed this prefactor from K(χ), since it is already in the expression of U(P).

The equations are now consistent with the expressions found in the articles Kirchhoff's diffraction formula and Fresnel diffraction. Edgar.bonet (talk) 15:02, 14 December 2012 (UTC)

References

Removal of recent additions which appear to contradict reference sources - and no references provided

Removed text in italics

(which in most cases is true - as was found later - due to superposition (=addition, or interference) of all primary, secondary, tretiary, etc waves) These assumptions have obvious physical foundation

Longhurst – “It is not made clear in the theory why the secondary sources produce no effect in the reverse direction”

Fresnel (not Huygens) was indeed able to predict the many aspects of wave propagation but only with the addition of arbitrary assumptions with no physical foundation

Born and Wolf: “The additional assumptions must, however, be regarded as a purley convenient way of interpreting the mathematical expressions, and as being devoid of physical significance”

I see no basis for the assumption that all waves propagate in a uniform sphere due to the "isotropy" of space. The only type of wave source which would propagate spherically would be an explosion, and that would only be due to multiple sources propagating simultaneously from the same point in all directions. The wave creating mechanisms, compression and rarefaction occur due to linear motions in some specific single direction. This is not something that would ever produce a uniform, symmetrical, spherical disturbance in all directions. — Preceding unsigned comment added by 107.77.199.210 (talk) 12:08, 20 July 2018 (UTC)

Huygens principle simply and elegantly explains many aspects of wave propagation, including diffraction.

Longhurst: “It (Huygens theory) was not sufficient to explain in detail the departures from exactly rectilinear propagation of light which are encountered in the cases of diffraction”

“Huygens principle follows from isotropy of space (or of media in which wave propagates): a local disturbance (which itself may be caused by a passing wave) propagates in all directions indiscriminately simply because all directions in isotropic media (or space) are equal.”

Cite a reference source to justify this statement - not mentioned in Born and Wolf, Longhurst, Heavens & Ditcuburn. The Kirchhoff's diffraction formula uses several approxomations in applying Green's theoem to the basic wave equation in whihc the arbitrary assumptions of Fresnel emerge out of the maths/physica rather then being plugged in to get the right answer.

and tertiary, etc) I find no mention of tertiary waves anywhere in the literature

Epzcaw (talk) 13:54, 11 May 2011 (UTC)

I have transferred the material about QED to a separate section, though I don't really see why it needs to be in the article at all. I have also amended some of the statement and improved the English.

It is incorrect to say that "The Huygens–Fresnel principle follows from isotropy of space" since Huygens-Fresnel has built-in anisotropy in the form of the inclination or obliquity factor. Huygen's principle does not imply isotropy either, since he builds in the incorrect assumption that there is no backward propagation, but if this is ignored, then I guess one could accept the statement that "The Huygens principle follows from isotropy of space". This needs to be backed up by a reliable source.

The statement that "Huygens–Fresnel principle is fundamental to quantum electrodynamics (QED)" has been amended to "The Huygens principle is fundamental to quantum electrodynamics (QED)". Again, this needs to be backed up by reference to a reliable source. Wikipedia is not there for the expression of individual opinions, but as an encylopedia of existing knowledge - see Wikipedia: simplified ruleset#Writing high quality articles

"Verifiability: Articles should contain only material that has been published by reliable sources. These are sources with a reputation for fact-checking and accuracy, like newspapers, academic journals, and books. Even if something is true our standards require it be published in a reliable source before it can be included. Editors should cite reliable sources for any material that is controversial or challenged, otherwise it may be removed by any editor. The obligation to provide a reliable source is on whoever wants to include material."

I'm not quite sure why the statement about the accuracy of QED is relevant here, but I have left it in place anyway. (It is quite impressive!!). Epzcaw (talk) 17:49, 13 May 2011 (UTC)

Removed a statement based on opinions

This is what I removed: The source further states though, "However, Schwartz was expressing the classical (i.e., late 19th century) view of electromagnetism. The propagation of light in quantum field theory actually is consistent with the very interpretation of Huygens’ principle that Schwartz regarded as nonsense."

This statement is debatable, and is an opinion of the writer of the article and not even of Schwartz https://en.wikipedia.org/wiki/Wikipedia:No_original_research

I doubt that a nobel prize in QFT as Schwartz does not have in mind first hand the QFT issues with wave/particle propagation in vacuum

In case anyone want it, the reference is here.. Gah4 (talk) 02:45, 13 March 2022 (UTC)

References

First observed when?

The article says "Lisle had observed this fifty years earlier [than Arago]" but our article for Arago spot has sources that say Joseph-Nicolas Delisle and Giacomo F. Maraldi independently observed it nearly a century before, not fifty years. Jason Quinn (talk) 15:16, 12 March 2022 (UTC)