# Talk:Huygens–Fresnel principle

## Criticism

A bit of a crap description, in my view at least. Put simply, Huygen's Principle is that a wave front can be thought of as infinite amount of point sources that produce spherical disturbances that reinforce to produce the secondary wavefront and so on. Although the author mentions how it is related to diffraction, he/she fails to explain how in any significant depth. I feel that too many people on Wikipedia (as brilliant a resource as it is) try to sound clever by using fancy language which at most times is inappropriate. `(posted anonymously, 21:21, 2 June 2005 129.67.48.245)`

### Be more specific in your critique

Actually I found this explanation fine, and I find Wikipedia to be a good resource in addition to others.

Although I understand your complaint in general, as this does happen (see next paragraph), you yourself did not add any value at all to the definition, nor go into even a decent level of detail on expanding the problems you had with it. Simplicity is good; but you still have to be artful in getting your point across. You didn't imho.

To add your own perspective is fine, but to blurt a brief complaint that has no depth or richness itself, frankly just makes you appear as actually the very kind of person that exploits what nominal personal knowledge you have on a subject for reasons of poor self-confidence.

Try to add useful criticisms with some depth instead of coming off, shall we say, a bit unpleasant?

mmf 06:30, 8 November 2005 (UTC) mmf

- FWIW, I think the description (as of Jul 2007) is really rather good. ErkDemon 17:23, 27 July 2007 (UTC)

## Query

I recently added a short section on the connection between Huygens Principle and the Greens function method. For classical and modern physics, the Huygens Principle and its connection to the Greens Function method is tremendously important. A good reference is The Mathematical Theory of Huygens' Principle (Paperback) by Bevan B. Baker, E. T. Copson. The section was removed without explanation. I do not want to add it again without discussion. Best, Rb

I didn't actually remove it, I integrated it into the previous section. I agree the connection is really important, and I'm glad you brought it up, I just think the current version reads easier. It seemed strange to have a separate section for 2 or 3 sentences. If you plan on expounding, by all means readd it.--Hyandat 19:57, 20 December 2005 (UTC)

## Link?

Thanks Hyandat, I just hadn't noticed. The article on Huygens himself does not mention the principle. Should a link be added there? Best, Rb

## Apostrophe or Hyphen has got to go

Shouldn't it be **Huygens-Fresnel principle**? *Huygens' Principle* makes sense, but when compounded the possessive should be on either both names (awkward, probably *Huygens' and Fresnel's principle*), or neither (*the Huygens-Fresnel principle*). If this is actually a "Fresnel principle" that belongs to Huygens, then the hyphen is wrong (*Huygens' Fresnel principle*). I'm not correcting this because I don't know the correct expression. edgarde 20:42, 5 June 2006 (UTC)

- Nope its Huygens-Fresnel Principle, I spent 2 months studying it at university! Rob.derosa 12:19, 25 June 2006 (UTC)
- Thanks for fixing this. edgarde 06:10, 7 July 2006 (UTC)

## di Groot's comment

[note by Siward de Groot: i do not agree with the claim that "the same is true of light passing the edge of an obstacle", because if light passes a narrow slit in vacuum, it causes diffraction bands, but there is no matter in the slit to act as secondary source of light. Rather, the explanation in this case is that:

if an (infinitely large) metal screen is between a source of light and a white wall, then there will be no light falling on the wall. This is because the electromagnetic force of the light acts on the wall, and it also acts on the metal shield, where it gives rise to a secondary electromagnetic force, that is the exact opposite of the original stimulus, so that on the light side of the screen reflected light is apparent, while on the wall side of the screen primary and secondary forces cancel out, so it is dark there.

The secundary force is due to the combined effect of all atoms of the screen. Now if a slit is made in this screen, all parts of this screen still experience the same primary stimulus, and therefore produce the same secondary response, except for the atoms that previously were where now the slit is. Thus the resulting lightness on the wall equals the secondary emission previously caused by these atoms, multiplied by -1 , for every point in time.

It is for this reason that the amplitude of the light apparent on that wall can be computed as if it were caused by secondary sources of light in the slit.]

Moved by --Hyandat 17:52, 23 July 2006 (UTC)

## Fourier transforms

Enormousdude, this section you're editing has more fundamental problems. First the Psi(r) should not be a function of r, but of the field location where you want the result (call it x or something); the r gets integrated out. Second, the integral assumes the functions add up all in the same direction, omitting the cos(theta) that Joe Goodman shows, here on page 66. Perhaps that's why it's a far-field approximation? It's not because all the points in the aperture are in phase; that works for near-field just as well, I think. How it becomes a Fourier transform is not explained at all; it comes from the x ocations off axis corresponding to gradients in r that through the exponential make the varying-frequency sinusoids. So you need to say something about how the r pattern depends on the field location x to get from far-field approximation to Fourier transform. The r in the denominator has negligible variation in the far field, which is why you end up with just the FT of the aperture shape. Dicklyon 00:30, 21 June 2007 (UTC)

## Direction dependance

As I understand it, the circular wavefronts coming from the infinity of points have different amplitude in different directions. In particular, if they have an amplitude of 1 in the forward direction it will be 0 in the reverse direction and in general have an amplitude of . 155.212.242.34 (talk) 20:49, 7 December 2007 (UTC)

## Reference

I am thinking about putting Max Born's book Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light under a new reference section because the book offers some good explanations about Huygens-Fresnel Principle. Bchen4 15:38, 5 March 2008 (UTC)

- I added a references section. But don't just add the book there; use it to add or support something in the article, and put it in a footnote. Let us know if you need help. Dicklyon (talk) 16:14, 5 March 2008 (UTC)

I have added a reference - it is a rather elderly optics book, but this is not a problem except that it may be hard to come by. I think Born and Wolf would be an excellent source - I do not, however, have a copy to hand and would not want to add the reference without being able to see the words directly in front of me. Epzcaw (talk) 19:15, 29 May 2008 (UTC)

I have now (some years on) added a section, as promised, called 'Mathematical expression of the principle' which is based on Born & Wolf's treatment - mathematically identical (as you would expect) to all the other optics textbooks that cover the subject that I have looked at. Epzcaw (talk) 08:31, 16 May 2011 (UTC)

## Merge with diffraction

I beleive that most of what is in this article is either in, or should be in the diffraction article. Epzcaw (talk) 20:35, 29 May 2008 (UTC)

- That may be so. But a separate article on this principle still makes sense, especially since it's so useful in general optical problems, as a way to explain rays, Snell's law, etc., not just diffraction. Dicklyon (talk) 20:58, 29 May 2008 (UTC)

I'm not sure what you mean by 'this principle'. Huygens-Fresnel principle is the the idea that each point on a wavefront is a source of secondary waves, which means that a wave is 'diffracted' rather than travelling a set of rays and does, as you say, explain many of the interesting things about how waves propagate, including a waves travelling through a slit, a circular aperture, a grating, a refracting medium and a lens, a wave interacting with a rough surface and a mirror surface, the changing profile of a laser beam, the structure of a focused laser beam, the otuput of an ultrasonic transducer, the receiving field of a radio wave antenna, etc. etc.

I think there is a lot of misunderstanding about diffraction - it is described by many people as 'the way light is bent when it encounters an obstacle', but diffraction, as defined by teh Huygens-Fresnel, or Fraunhoffer, or any other diffraciton integral, relates not just to this but to general wave propagation.

Perhaps the problem lies in the definition of diffraction. Epzcaw (talk) 23:47, 30 May 2008 (UTC)

- No, there's no problem with diffraction. My point is that the H-F principle also explains the normal straight-line propagation of light, the reflection and refraction of rays, and stuff like that that is not generally considered under "diffraction". Huygens even used it to explain the anomalous refraction of Iceland spar. Dicklyon (talk) 00:07, 31 May 2008 (UTC)

'Stuff that is not normally considered under 'diffraction' is exactly my point. Huygens-Fresnel IS diffraction; the Huyges-Fresnel and diffraction articles have several items in common, and rightly so, so shouldn't they be one and the same, and should include all the aspects mentioned above, or perhaps link to new pages covering specific aspects. Diffraction is nto some magical thing that happens when a wave hits an object, it is an in-built feature of wave propagation.

I will maybe have a go at drafting something on my user page, and you could comment on that. But for a week or twoEpzcaw (talk) 06:59, 31 May 2008 (UTC)

Have changed my mind about merge - have redited 'Diffraction' in such a way that this article does not overlap significantly. —Preceding unsigned comment added by Epzcaw (talk • contribs) 17:10, 3 June 2008 (UTC)

## Wavefronts

The term "wavefront" is not at all well defined. 3piecesuits (talk) 16:11, 10 November 2008 (UTC)

## Classical wave theory approach

The Huygen-Fresnel principle might well now be a "method of analysis" but it is also a fundamental building block of classical wave theory, to state "Huygens principle follows formally from the fundamental postulate of quantum electrodynamics" is chronologically misleading in the extreme, the principle itself can be used to derive Snell's law and this was fundamentally important to the wide acceptance of a wave theory of light pre wave-particle duality. Whilst reformulating all physics as following from quantum theory is commedable it is hardly helpful when people wish to investigate a more historical evolution. Perhaps acknowledging its historical uses as well as its modern applications would be appropriate considering the number of people who use wikipedia as a resource for rather lower level work than fourier optics? —Preceding unsigned comment added by 144.173.54.122 (talk) 16:25, 18 March 2009 (UTC)

I would like to add to this comment. It is misleading to imply that historically important aspects of classical wave theory are quantum-theoretical in nature. Actually, it is convenient, within quantum theory, to treat the electromagnetic field classically, and insert the quantum-theoretical photon anhillation and creation operators later when needed [J.A. Wheeler, Mathematical Foundations of Quantum Mechanics, edited by A.R. Marlow (New York, Academic Press, 1978), pp. 15-16]. (Wheeler cited Heisenberg and Pauli regarding this.)

(Being somewhat illiterate of the intricacies of adding comments, I apologize if this is not the right way of inserting my comment. I hope this spurs someone to make the indicated corrections.) James R. Johnston, Ph.D. —Preceding unsigned comment added by 24.130.242.67 (talk) 08:50, 13 July 2009 (UTC)

I totally agree, I think that it is not only historically incorrect, but also physically incorrect. Diffraction also occurs in other classical waves, like sound, waves in water, not just light and matter. I think it is not necessary to introduce QED in order to demonstrate the Huygens-Fresnel principle. I've never actually demonstrated it, but I think it should be demonstrable just by using the wave equations, by thinking in the characteristic lines of the parabolic differential equation that "propagate" the wave in every direction, or something like that. —Preceding unsigned comment added by 190.21.226.231 (talk) 01:45, 27 August 2009 (UTC)

## Expansion of article

I have expanded the article to include detail about Huygen's work, and Fresnel's development of it. I have also explained the limitations of the Huygens-Fresnel principle - it is not very satisfactory, as it involves several arbitrary assumptions and an undefined inclination factor. I have also included the theory behind the principle; this is based closely (but not exactly!)on Born & Wolf's treatment.

I have removed the sentence about its elegance, as I don't think that this can be applied to it. Obviously, it was very clever in its time, but I think the accoldate should go to Kirchoff's diffraction formula, which does not appear anywhere in Wikipedia at the moment. I hope to rectify this soon. Epzcaw (talk) 17:27, 20 April 2011 (UTC)

## Reverted

I reverted a couple of recent edits that were mostly about putting LaTeX math mode into sentences. This is generally frowned on. Use ordinary html, or even better, the Template:Math version, which looks good in sentences but uses the same font as math. Also there were changes to the use of the term "amplitude"; it's used in two ways, but I don't think the fix was great. I'd keep amplitude for the U factor and use something else for the instantaneous wave value. Dicklyon (talk) 23:59, 22 April 2011 (UTC)

......

Sorry - I misundertood instructions about maths - I thought someone (you?) said they should be in LaTex within text.

Re amplitude - Born and Wolf use the term 'disturbance' for the instantaneous wave value. What do you think about following this. Amplitude would then refer solely to the magnitude of the disturbance. Epzcaw (talk) 14:21, 23 April 2011 (UTC)

The second section would then read as follows:

- I don't want to get into this argument again - what's in a name?. So just refer to the absolute value of the complex amplitude as the 'magnitude'. The disturbance can become 'amplitude' again, or it can stay as 'disturbance' to avoid confusion to those people who consider the amplitude to mean the magnitude as explained in this Wikipedia article. The latter he been implemented below. Epzcaw (talk) 19:01, 23 April 2011 (UTC)
- Have put 'magnitude' instead of 'amplitude' where relevant, anc 'complex amplitude' also where relevant. I hope that this is non-controversial. Epzcaw (talk) 15:33, 24 April 2011 (UTC)

## Mathematical expression of the principle

Consider the case of a point source located at a point *P _{0}* vibrating at a frequency

*f*, where the disturbance is described by a complex variable

*U*. It generates a spherical wave with wavelength λ, wavenumber

_{0}*k*= 2π/λ. The primary wave disturbance at the point

*Q*located at a distance r

_{0}from

*P*is given by

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 r_{0}. 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:

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,^{[1]} 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,^{[1]} to which the Huygens–Fresnel principle can be considered to be an approximation. Kirchoff gives the following epxression for K(χ):

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*).

- I changed the sign of the prefactor which now is −
- 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)

## 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”

*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)

## Requests

Could the years when Huygens and Fresnel proposed their theories be added to the history section to provide a sense of how long it took for the theory to evolve? Also, it might be necessary to clarify, how Huygens's method of summing spherical waves is different from Fresnel's principle of interference. From the current text it isn't clear what Fresnel's contribution exactly was. I don't know enough about the subject to make the additions myself, but could someone else look at them at their leisure? — Preceding unsigned comment added by 130.233.155.47 (talk) 10:02, 26 April 2012 (UTC)

- I have added dates, as requested above.
- I am thinking about how the second point can be addressed - it is a valid question. It may be that a seperate article discussing Huygen's theory of light is required, or it may be possible just to expand on what is in this one. Epzcaw (talk) 13:06, 7 May 2012 (UTC)

## Quest II

Can anybody tell if Kirchhoff's diffraction formula implicates that the light or any other wave do travel backwards being π/2 < χ < π ? If that is the case that would be remarkable (not sure if that is the correct word) on the apropiate section (Mathematical expression of the principle). It would be useful if anybody could concretely state it, cause saying that "...however, K is not equal to zero at χ = π/2 " is not enough! .

Also it should be stated, if that is the case, that Kirchhoff's diffraction formula is more exact than Huygens–Fresnel principle and dont leave it at reader's assumption. Thanks FranJH — Preceding unsigned comment added by 201.231.51.236 (talk) 22:33, 18 November 2012 (UTC)

- ↑
^{1.0}^{1.1}Cite error: Invalid`<ref>`

tag; no text was provided for refs named`Born and Wolf`