# A variation on the Fresnel Spot experiment

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Hello

Fresnel discovered that the shadow of a small disc had a bright point in its center. Experiment that he carried out by letting sunlight pass through a small hole (quasi-point source).

If, instead of looking at the shadow of the disk, we look (*) in the direction of the light source, hidden by the disk, what do we see?
Nothing? A bright ring around the disc? Something else?

(*) Or a long exposure with a camera

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I think we will see the edge of the disc dimly lit up. The edge of the disc is the source of the diffracted rays.

Hello

That's what I think too but I couldn't find any reference in the literature. I don't think anyone has had this experience.

If we see the edge of the disc dimly lit up, can we say that the light is deviated in the shadow of the disk?
And if we vary the distance between the disc and the eye of the observer, does the observed figure (the light around the disc) remain constant?

Don't you think this experiment is worth doing? We can also consider the same with the shadow of the edge of a "right" screen. Easier to experiment

I don't forget that until now, light has two natures. Wave and particle...

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This is just my personal view on this, but I think the diffraction happens because the light hitting the disc causes movement of the electrons, or the flow of currents, on the surface of the disc. These currents cause re-radiation; the electrons on the edge of the disc re-radiate in all directions, and some of this is towards the shadow area, where we see it as diffacted energy. If we are within the shadow area and we go closer to the disc, the energy being diffracted in our direction will reduce because it has to bend through a larger angle. On the other hand, as we go further from the disc, the amount of diffraction increases until eventually the disc is having almost no effect. It is noticeable that the rippling effect seen outside the diameter of the disc is not seen within the shadow, where the illumination tapers smoothly towards the edges. The type of edge, whether rounded or knife edge, also affects the intensity. It is a complex subject for mathematics, beyond me, and very interesting for experiment. It is possible to carry out experiments using microwaves quite easily.

Hello Tech99

To calculate the luminous intensity on the observation screen (when looking at the shadow) Fresnel (and books on wave optics) do not take into account the "shape" of the edge of the disc. Fresnel used not a disc, but an opaque sphere. The results are similar with a disc, I think. These are the dimensions (distances, diameter, wavelength) which make it possible to calculate, among other things, the distance between the maximum luminosity of the interferences. Below is the light intensity near the edge of a screen. (when looking at the shadow); The black line represents the limit of the geometric shadow.

There is, in the history of physics, an experiment where we are interested in the origin of light. And therefore its possible deviation. Realized for the first time by Eddington in 1919. The first luminous ring observed was in 1987, at the Very Large Array by a group of scientists led by Jacqueline Hewitt. But here the origin of the deviation is gravitational. It is not diffraction.

Photograph of Eddington and light ring:

Have a nice day

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Gravitational lensing is not the same as diffraction. It works in the ray optics approximation, which diffraction does not.

What you would see if you put your eye where the Fresnel spot is depends a bit on details of the optical system, I think - in particular the diameter of the pupil with respect to the typical scale of the pattern. I think you should see roughly the Fourier transform of the light distribution on the pupil, but there's significant phase variation in a Fresnel pattern so it isn't necessarily simple to work out what that is.

I don't think it would be particularly difficult to do the experiment if you wanted to, although as a safety measure I'd recommend using a camera instead of your eye. Its optics are similar, and staring down laser beams is not recommended even if you are certain they're class I.

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Hello Tech99

To calculate the luminous intensity on the observation screen (when looking at the shadow) Fresnel (and books on wave optics) do not take into account the "shape" of the edge of the disc. Fresnel used not a disc, but an opaque sphere. The results are similar with a disc, I think. These are the dimensions (distances, diameter, wavelength) which make it possible to calculate, among other things, the distance between the maximum luminosity of the interferences. Below is the light intensity near the edge of a screen. (when looking at the shadow); The black line represents the limit of the geometric shadow.

View attachment 299302

There is, in the history of physics, an experiment where we are interested in the origin of light. And therefore its possible deviation. Realized for the first time by Eddington in 1919. The first luminous ring observed was in 1987, at the Very Large Array by a group of scientists led by Jacqueline Hewitt. But here the origin of the deviation is gravitational. It is not diffraction.

Photograph of Eddington and light ring:

View attachment 299303

View attachment 299304

Have a nice day

Can you tell me what the second picture is, as it displays a bright spot at the centre of the disc. I presume this is gravitational lensing.

Hello Tech 99

This photo is captioned: This image shows an Einstein ring (middle right), which occurs when a massive object acts as a lens. This phenomenon is known as gravitational lensing and you will find another example in the Guru's article: “An Einstein Ring Spawned by Galaxy Warping of Space”. (ESA / Hubble & NASA)

In diffraction, light enters the shadow of opaque objects. And it seems to me that in the gravitational deviation, it's the same. Even if the causes are different. Bernadette

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For a lens, rays which arrive at the lens parallel to the axis are bent so tat they all pass through a focal point. For diffraction, such parallel rays are not bent in a fixed direction but are scattered over a wide range of angles, so that there is no defined focal point.

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Even if the causes are different.
It isn't that the causes are different that makes the question tricky to answer, it's that the nature of the light arriving at the image plane is very different. Gravitationally lensed light is incoherent - light taking different paths around an object may take centuries more going round one side or the other. The phase structure of arriving light isn't well defined.

But a Fresnel spot is a diffraction effect. It requires coherent illumination and there is a phase structure and that can matter for what happens downstream in further optics that you put in.

Less technically, in gravitational lensing you can just model light as traveling in straight lines by the time it reaches your eye. Not so in the Fresnel case.

Hello Tech 99 and Ibix

Thanks for the exchange. It's interesting.

From what I know...

In his treatise "optics" (1704 in English), Newton suggests that light is made up of material particles. Cautious, his name does not appear on the cover of his book... (sometimes added by hand)
Huyghens publishes his "treatise on the light" in 1690 (in French!) in a form still very little developed and quickly eclipsed by Newtonian successes...
Fresnel took up the work of Huygens in 1815 as the starting point for his research on the diffraction of light.
And in 1905 Einstein takes up the notion of particle of light (and quantum of energy introduced by Planck in 1900 to explain the emission of the black body) to explain the photoelectric emission.

Huyghens' theory is quite simple: light is a wave, and each point reached by the light (the wave) can be considered as a source (read Feynman concerning the shadow of the edge of a straight screen).
For the theory of the grational deviation, there is no formula describing an attraction by the mass which deviates the light ray (the photons therefore). It is the notion of the geodesic of space/time that must be considered. And a good mathematical background is necessary.

At any rate.
Experimenting with gravitational deviation is done by looking at where the light comes from.
And that of diffraction where it arrives.
In the case of diffraction, informations could be obtained by looking at where it comes from.

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I think you're missing the point.

In both gravitational lensing and diffraction cases you can model light as a wave and determine its propagation. But there's no point in doing so in the gravitational lens case because the scales are so huge that the results are indistinguishable from the ray approximation. That is not the case for Fresnel diffraction, where you are close enough to the obstruction that the non-ray-like behaviour of the wave model is needed.

The point is that in the diffraction case "where the light comes from" isn't particularly clearly defined. You can't ray-trace a bright spot backwards to some point around the obstruction because light isn't behaving as a ray - you need the full wave model to describe it (or at least the Fresnel approximation to the full wave model). In gravitational lensing ray tracing is sufficient, albeit made more complex by the curvature of spacetime.

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No need to guess. This has been done. See the following video by The Action Lab at the 5:45 and 7:00 marks.

DrClaude, Klystron and Ibix
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I would like to see the experiment for spheres having both a silver surface and one coated with lamp black.
Also I would like to see the result for linearly polarised light.

I would like to see the experiment for spheres having both a silver surface and one coated with lamp black.
Also I would like to see the result for linearly polarised light.
Hello Tech99

I read Fresnel quite a while ago. He meticulously describes the experiments he has carried out. But I don't remember him talking about those kinds of details. I did some diffraction experiments myself and found it to be a good way to make objects that intercept part of the light opaque. Blacken them using a candle (black body in the sense of Planck). A silvery surface returns the light it receives and this interferes with observing the shadow. Fresnel also used a pane on which he deposited Indian ink. This allowed him to create very fine slits. The question I asked was to know what we saw if we looked towards the source of light hidden by the diffracting object. But the further I go, the more I realize that this kind of experience has never been done.

Have a nice day

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But the further I go, the more I realize that this kind of experience has never been done.
Apart from in the video Drakkith posted, of course...

Gold Member
I looked at the video. When he looks through the pin hole at the scene, it does not tell us very much. We see the ordinary room, not interrupted by the sphere, and where the sphere is located we see a blob of light. The camera is overloaded and I think we would like to see the sphere and its illumination in more detail.
In your own experiments, when you changed from a silver to a black sphere, it sounds as if the silver one had more diffracted energy.

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But the further I go, the more I realize that this kind of experience has never been done.
I'd bet my left leg that this experiment has been done many times with various coatings and with various types of lights, including polarized. The hard part is finding the writings from those few people who actually wrote everything down.

When he looks through the pin hole at the scene, it does not tell us very much. We see the ordinary room, not interrupted by the sphere, and where the sphere is located we see a blob of light. The camera is overloaded and I think we would like to see the sphere and its illumination in more detail.
The entire setup is shown in the video. What more do you want?

sophiecentaur
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I would like the camera exposure to be turned down so we can see if the light comes from the edges of the sphere; at the moment I just see a blob of light.

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I would like the camera exposure to be turned down so we can see if the light comes from the edges of the sphere; at the moment I just see a blob of light.
While there may be some residual light from diffraction, the light that forms the spot will not look as if it came from the edge of the sphere. For that to be the case the light would have to form a ring on the detector, not a spot.

Edit: I'm not confident that what I just said is correct, so please ignore me. I'm leaving this post here for continuity of the thread.

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Apart from in the video Drakkith posted, of course...
I think the video shows the experiment that Fresnel did around 1800. It's a shame the image isn't sharper when he points his camera at the light source.

I would like the camera exposure to be turned down so we can see if the light comes from the edges of the sphere; at the moment I just see a blob of light.
I think so too

Hello Drakkith

You write: "the light that forms the spot will not look as if it came from the edge of the sphere"

Do you speak of the spot in the center of the shadow?

If we follow Huyghens' theory (each point reached by the light wave can be considered as a source), each point in space in a plane passing through the sphere (plane perpendicular to the source/sphere direction) is a source . And so we should see a "halo" of light around the sphere, brighter the closer we are to the edge of the sphere. But I think that we must also integrate into this what happens in the detector: the eye or the camera ..... oups .

Nice wednesday

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And so we should see a "halo" of light around the sphere, brighter the closer we are to the edge of the sphere.
Hmm. After thinking it over more I'm not confident in my last post. I was thinking that whatever was on the screen would be what you would see in the camera. But I didn't take the camera's lens into account. You might very well see a bright ring around the sphere.

A good example of the phrase, "Knowing enough to get yourself into trouble."

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But I didn't take the camera's lens into account. You might very well see a bright ring around the sphere.
In the image plane you should see something like the Fourier transform of the light distribution in the lens plane. Since there's quite a lot of phase structure there, I think what you see would depend a lot on the camera's characteristics - notably the aperture diameter compared to the pattern scale.

tech99 and Drakkith
Gold Member
I am likely wrong here, but it occurred to me that when we are close to the sphere, the Fresnel Spot must have a surrounding ring where the light from one side of the disc is an increment of a whole wavelength delayed relative to the other.

Hello Tech99.

Fresnel Spot:
1. Simulation

The image above shows a numerical simulation of the Fresnel spot in the shadow of a disk (diaphragm) with a diameter of 2 mm, at a distance of 1 m from the disk. The light source is a helium-neon laser which emits in the red (λ = 633 nm) and is located 1 m from the opaque circular obstacle. The actual width of this diffraction pattern is 16 mm. (Google traduction...)

2/Reality

View attachment tache-de-poisson.webp

Oups............
More difficult in the reality...

End day here for me. There are more simulations on the wikipedia English page (than on french one...) (https://en.wikipedia.org/wiki/Arago_spot)

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On the simulation, by enlarging the image I can see rings going right into the centre.

Hello Tech99.

You are rigth. For the simulation... Some other pictures.

(from wikipedia English. Arago spot.

I have make some "trials" time ago (we don't have camera like now...). I think i will perform some and use a glass sheet (like Fresnel with Chinese ink) but with a small round stickers. And try to get photography of the shadow and photography in the other direction (from where ligth comes).

Have a nice Thursday

Gold Member
I think we see inner rings when the screen is closer to the sphere that the Rayleigh Distance = diameter/ 2 pi lambda.
Ironic that to see a spot with no rings we must be outside the Fresnel Region.

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the light hitting the disc causes movement of the electrons, or the flow of currents, on the surface of the disc.
I don't think the details of the mechanism relevant (first order). A conducting or non conducting obstacle will both produce the effect. The limits of a simple definite integral will do for predicting the spot size.
Edit: I'm not confident that what I just said is correct, so please ignore me. I'm leaving this post here for continuity of the thread.
I think you are right to strike it through. Just think how, when you look at an object in a lens, you see the object somewhere in the centre and not 'from any particular part of the lens'. What you see is a result of diffraction (yes - diffraction from all over the lens is a 'thing'). It even works with a stereo pair of speakers; the image is perceived as in the middle - where there's nothing.

With an obscuring a beam with a disc, the resulting spot is very faint and a normal camera sensor will not have the contrast capabilities to handle the range but multiple exposures can be stacked to produce a highly enhanced contrast ratio (which can be gamma'd to display the whole range). It will have been done many times.

Thanks Sophie

In the usual experience of the shadow of a disc, we look at this shadow (and its central point...). The question was: what do we see when looking towards the source of light hidden by the disc? In diffraction, light is considered to be a wave. This makes it possible to "understand", to calculate the intensity of light at each point of the shadow. In other experiments on light, we look in the direction of the source of light, and we look where it comes from; and possibly whether it has been diverted. And the light is in these experiences, considered as a particle. The question was therefore to design an experience where we can both look at where the light comes from and where it arrives. That of the Fresnel spot seems appropriate to me.

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Remember, however, that in order to resolve an image of the disc, the detector cannot be a point, but must have finite dimensions. The detector itself is then subject to interference effects, so the disc must be large enough to allow an effective directional detector to be employed.

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