Solar corona Cloud iridescence

I am afraid that this is not a very good picture, first because the colors are not very well defined and second because I could not find a single, smallish object with which to block the sun, so I had to settle for this tree.

I could not immediately find a halfway decent explanation of cloud iridescence. Wikipedia says it is a diffraction phenomenon, with no elaboration. Here is what I think is going on.

I do not feel like drawing any cartoons, so please have a look at the Wikipedia article on the Airy disk. About 2/3 of the way down, you will see a plot of intensity as a function of angle. This plot represents the diffraction pattern of a circular aperture. The pattern shows a series of secondary maxima at various angles off axis. The first secondary maximum has an intensity of approximately 2 % of the intensity at 0.

What has the Airy disk to do with iridescence? Oddly, the diffraction pattern of a circular obstacle is the same as that of a circular aperture, except near 0. If the cloud cover is thin enough and the droplets are all approximately the same diameter, we may see colored fringes, because we are standing at the location of the first secondary maximum of a particular wavelength. The angle 0 in the Wikipedia figure is the line between the sun and a droplet; it is not directly in line with the sun from our point of view. We may see several different colors because the secondary maxima of different wavelengths appear at different angles.

In the picture above, we do not see colors very clearly, most probably because the droplets do not have the same diameter. However, because the cloud is between us and the sun, we see a circular halo all the way around the sun, which suggests to me that the droplets are spherical and (I would guess) liquid water rather than ice crystals. (Ice crystals like to be snowflakes, hexagonal cylinders, or flat hexagonal plates. These are oriented by viscous forces, so the scattering pattern would not demonstrate circular symmetry.)

Finally, if you look to the right of the first ring of colored fringes, you will see a second partial ring, which represents the second secondary maximum of the diffraction pattern.

Is this really Cloud Irridescence or is it a sun halo? I think the two are different phenomena, are they not? The fact this this is centered on the sun in a ring suggests the latter to me.

There is an interesting little demonstration one can do with an overhead projector with a hole in a piece of black paper and with its inverse, i.e., a black dot. A similar demonstration can be done with a single slit and its inverse, a strip of black paper.

The hole and the slit have Fourier transforms of J1(r)/r and sin(x)/x respectively, were J1 is the Bessel function of the first kind, order 1. (I didn’t put the wavelength dependence into those expressions, but each wavelength will diffract at a different angle.)

The interesting part is that the inverses have the same transforms but with a phase shift such that the resulting spectra come out with the complementary colors of the rainbow.

In order to do the demonstration with the inverse hole and slit, it is important to reduce the bright ambient light coming from around the inverse hole or slit because all that extra light washes out the colors so they are hard to see. This means adding a fairly large aperture between the focusing lens and the screen or between the Fresnel lens and the focusing lens. You have to play around with the position of the aperture in order to see the color spectra and be able to notice that they are the complementary colors. Because of the ambient light, the complementary colors will seem to be “pastel;” that’s what adding white light to a spectrum does.

I have done this classroom demonstration quite a number of times; and it is important for the room to be dark. The eye has a tendency to “compensate” so it is easy to be fooled into thinking that the inverses produce the same specta as the hole and the slit. Setting up two projectors next to each other and alternately blocking their light allows one to switch back and forth to see that the spectra are indeed complementary.

The holes and slits - and their inverses - that I used were approximately 3 - 5 mm in diameter and width. You also need a projector that has a pretty broad and bright white light spectrum; don’t use one with a dim, yellowish bulb.

I do not think it is a halo – halos and rainbows are sharper. This pattern looks like a simple diffraction pattern, not a caustic like a rainbow. But I am not an expert on these things. I will see whether I can find the metadata on the picture and maybe measure the angle, but do not hold your breath.

The electric field in the diffraction pattern of the opaque or complementary screen indeed has a phase shift of π, but I do not see how that phase shift is relevant. If I understand the experiment correctly, you see the diffraction pattern superimposed on a bright background from the near field of the projection lens. I would expect those to be incoherent and suspect that the colors are the result of some kind of ordinary color mizing. But I have not done the experiment and may misunderstand something.

Matt Young said:

The electric field in the diffraction pattern of the opaque or complementary screen indeed has a phase shift of π, but I do not see how that phase shift is relevant. If I understand the experiment correctly, you see the diffraction pattern superimposed on a bright background from the near field of the projection lens. I would expect those to be incoherent and suspect that the colors are the result of some kind of ordinary color mizing. But I have not done the experiment and may misunderstand something.

The last time I did it was the year I finally fully retired in 2004.

I don’t have access to an overhead projector now, and I am not sure that they are still in use since the availability of other projectors that hook up to a computer. I think one would have to use some additional lenses with such a projector; but one could use PowerPoint or some other program like Paint to make the slit and anti-slit. And I am not sure how this would work with an LED light source.

If you try the experiment, start with the slit and “anti-slit” first. The results are brighter. I ran the slit the full depth of the overhead projector (vertical on the screen).

The dot diffraction pattern is more difficult to see because there is so much light.

You can find a halfway-decent sketch showing how the 22-degree halo is formed here. Just Google words something like solar halo 22 degree hexagon, go to Images, and you will see a raft of photographs of complete halos, sun dogs, and other phenomena. The halo, like the rainbow, is a refraction phenomenon, including what is in essence chromatic aberration. The halo is therefore comparatively sharp, whereas the putative iridescence in my photograph is blurred and looks like a pure diffraction phenomenon.

I was incorrect in saying that hexagonal crystals usually orient themselves, by the way; I should probably have said they frequently orient themselves. When they are oriented, we see, for example, sun dogs, whereas when they are not oriented, we see full 360-degree halos and more. It is possible that the iridescence in the photograph is caused by randomly oriented ice crystals, I suppose, but then I would have expected to see a sharper circle.

OK, I went out and bought a copy of Robert Greenler’s Rainbows, Halos, and Glories. It is worth having even if all you do is look at the color plates. At any rate, the phenomenon in this photograph is called a solar corona; lunar coronas are more commonly seen because the sun is blinding. The corona is caused about as I described, and it is physically the same phenomenon as cloud iridescence, except that the distribution of droplet sizes is irregular around the edge of the cloud, where you are apt to see iridescence. I will change the headline of this article momentarily.