My friend noticed an interference-like pattern around the table leg. However, we do know that interference patterns of sunlight produces rainbow colours. What seems to be happening here?


These are probably caused by minute, periodic variations in the diameter of the table leg, formed by drawing through a die. Any vibration in the process would end up being circumferential waves in the surface of the tube. Changes in the diameter mean changes in the slope of the surface, and thus focus the reflected light to different rings around the base of the leg.

You could probably confirm this by shining a laser pointer at the leg and slowly moving it down along the leg; the reflected point on the ground will move periodically, pausing when it's moving down across a concave (along the axis) portion of the leg, and moving quickly when it's moving down along a convex portion.

Where the reflected laser pauses is where a broad beam of light would be focused and brighter; where the reflection moves quickly is where the beam of light would be diffused and darker.

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    $\begingroup$ If you don't have a laser, the shadow of your hand will behave the same way. $\endgroup$ – Beta Sep 27 '15 at 3:59
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    $\begingroup$ @Beta C'mon: you gotta use lasers whenever possible in physics... $\endgroup$ – Daniel Griscom Sep 27 '15 at 18:05
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    $\begingroup$ @DanielGriscom On the other hand, "if you don't have a laser, use your hand" is something I don't expect to see very often, and it should be cherished. $\endgroup$ – JiK Sep 28 '15 at 12:32
  • $\begingroup$ Periodic variations in specularity would also explain it, and would produce bands of even width, regardless of the distance to the floor. Variations in thickness would require the focal length to vary as well to produce that. Okham's razor? $\endgroup$ – Previous May 27 '16 at 16:26
  • $\begingroup$ @Previous The leg seems pretty evenly shiny, so specularity isn't the cause. (And, it's Occam's razor...) $\endgroup$ – Daniel Griscom May 27 '16 at 18:44

This is a grossly exaggerated illustration of a strictly cylindrical metal tube compared to a cylindrical tube with external diameter variations, like the one you have in your case:

enter image description here

Because of those diameter variations, the reflected light can vary between scattering and concentrating on the surfaces it is reflected onto.

bonus reflection gif: http://i.imgur.com/vunHHRA.gif

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  • $\begingroup$ So why do the reflections go all the way around the leg, staying uniform until it's lost in the direct sun? $\endgroup$ – JDługosz Sep 29 '15 at 6:37
  • $\begingroup$ @JDługosz: Perhaps this post can help. $\endgroup$ – Kyle Kanos Sep 29 '15 at 22:12
  • $\begingroup$ @JDługosz from the linked post you can see that when light from the sun hits a point anywhere on the surface of the cylinder, it reflects the rays in all directions, which results in the gradually decreasing portion of reflected rays going almost all the way to the shadow cast by the cylinder. $\endgroup$ – user1306322 Sep 30 '15 at 1:28

These are because the leg isn't exactly cylindrical. Here's a way to think about it (slightly different but the gist is there)

Imagine you have some pastry being squeezed through one (or two) rollers.

The pastry resists and builds up behind the rollers UNTIL enough of the pastry is touching the roller's surface that friction drags the pastry under, thus we go from thick to thin.

There are many ways to make tubes, most of which involve rolling a sheet thinner and thinner, it is the same principle.

Metal sheets have wavelengths like this, as does playdough, pastry (obviously!) but also interestingly enough so does paper.

Anything forced through rollers will build up on one side until friction drags it through and the connective forces inside the material "pull" some through.

I wish I could make gifs.

Picture may help (will add more later, really busy, if anyone else knows an image or a gif please do edit)

enter image description here

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  • $\begingroup$ Whaaaa? This makes no sense at any level. $\endgroup$ – Carl Witthoft Sep 26 '15 at 20:16
  • $\begingroup$ @CarlWitthoft I could explain with hand gestures. (not as in middle finger, genuinely, I could explain with hand gestures) $\endgroup$ – Alec Teal Sep 26 '15 at 20:26
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    $\begingroup$ @CarlWitthoft: Why not? $\endgroup$ – Lightness Races in Orbit Sep 26 '15 at 21:42
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    $\begingroup$ Despite the difficulty in describing how it happens, this gets closest to answering the question. However, here, I don't think we can be talking about rollers, since it is a tube. Also, I wonder that there may be both pushing and drawing forces on the tube (through a die?) That would more readily tie together the explanation you've started. $\endgroup$ – New Alexandria Sep 27 '15 at 14:37
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    $\begingroup$ @AlecTeal Tubes can be formed by extrusion. A web search will provide many examples. However, I agree that the tubing as shown was probably formed from a sheet - a look inside it to find the seam would confirm that. $\endgroup$ – Andrew Morton Sep 27 '15 at 17:35

This case is about reflection, not refraction. As the sun's light rays are reflected at different angles from the leg, some will interfere with each other constructively (forming light rings) and destructively (forming dark rings).

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I'm not convinced that variations in thickness are the cause. Variations in gloss (areas of specular reflection and areas of diffuse reflection) seem more likely: the "distribution requirements" are the same (in both cases the "defect" has to repeat at about equal distances), but the "thickness" hypothesis also requires that the curvature of the sections changes with height (because the focal length has to be proportional to the radius of the circles we see).

Edit: It looks like concentric circles, but a single spiral would look the same. A regular helix pattern of increased specularity would produce such an image. And a regular helix pattern is exactly what one can expect from the polishing process, in which pipes are rotated while they move along the grinding/polishing wheel or belt. While the process can be tuned to minimize them, periodic variations are an essential feature of that process: the center of the grinding/polishing wheel or belt moves in a helix over the surface of the pipe.

Such a helix of higher specularity will produce a regular spiral image regardless of the width and the spacing, or the position of the sun.

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