Yesterday evening, I saw a rather remarkable rainbow out my window. Both the primary and secondary bow were visible for their entire length, the sun was low in the sky, so it was almost a full half-circle, and it was crossed by converging sunbeams.
OK, that’s all very spectacular, but I understand all of that. What I’m wondering about, though, is the color sequence. As with any rainbow, it had the standard progression of red-orange-yellow-green-blue-purple, but then, below the “normal” purple band, there was another green band and another purple band. Actually, it looked like there might have been a whole complete extra sequence there, but the green and the purple were most distinct. These extra bands were flush with the bottom of the “normal” bands, and the total thickness of the “extra” bands was about half or two-thirds that of the primary bands. This was only visible on the left end of the rainbow, which happened to be the brightest and easiest to see out my windows. Due to faintness and the placement of my windows, I couldn’t clearly see where or how the extra bands ended in the middle, but they definitely weren’t present on the right end.
I was not under the influence of alcohol, nor any other hallucinogenic or mind-altering substance, and I’m not naturally prone to hallucinations.
Of course, something like this would happen when I don’t have any film in my camera, nor any available to put in.
As an aside, I wonder if this type of event, with the colors involved, is photographable??
I remember trying to photograph a sunset in the Grand Canyon some years ago, and, when I got my pictures back, the subtle hues of the purple/violet/reds weren’t there. MY eye could see them but the film couldn’t capture them. Why was that?
Such a thing is photographable, but I’m willing to bet you were using print film. Though print film has a wider lattitude for exposure, I’d try shooting a rainbow with slide film; that way the camera exposures that I make are there on the film, I’m not relying on a minilab machine to autoprint all my negs.
Chances are you might have something usable, with your sunset pictures as well, they were just not printed correctly. I’d also bracket my exposures; i.e., make 3 shots. One at the camera’s metering, one over, and one under.
I’ve got photos of supernumerary bows. I used to buy rainbow calendars to get illustrations for my lectures on rainbows.
The best book I’ve found on supernumerary rainbows is R.A.R. TRicker’s Introduction to Meteorological Optics. He gives you a full mathematical treatment.
Ultimately, you hve to realize that, although everyone treats rainbows as if they were a refractive phenomnon, a rainbow is really an interference/diffractive phenomenon – there are two different ray paths through the spherical raindrop that emerge at the same angle. But their path lengths are different, and they are different by a length smaller than the coherence length of the sunlight, so they interfere constructively or destructively. The first persomn to realize this as Thomas Young – who was obsessed with proving the wave nature of light, and was always looking for examples proving it (he’s most noted for the two-slit “Young’s experiment”). Unfortunately, he didn’t have the matrhematical oomph to prove his case with the rainbow (See C.B. Boyer’s book The Rainbow: From Myth to Mathematics). The mth was finally derived by George Biddel Airy, the director of the Royal Observatory in Greenwich. He gave us Airy’s Ranbow Integral, which Tricker derives in a much simpler form.
Because the path length difference varies with the size of the raindrop,the appearance of the rainbow depends upon raindrop size. See M. Minnaert’s classic book The Nature of Light and Clor in the Open Air for table that shows how you can deduce the size of the raindrop from the appearance of the rainbow. (If the geometrical optics/refractive explanation were all there was to it, the size of the drop would be irelevant to the apearance).
I’m sorry that I’ve never encountered an optics course or text that gave a proper explanation of the rainbow. I tried to present all this when I gave a course in optics at the University of Utah for a few years in the '80’s. I also did the same at Tufts about 1989.
Sounds like Fresnel Diffraction. It happens when the rainbow is created by very small raindrops. If the raindrops are large, you’ll see only the usual rainbow.
Here’s how to think about this. Suppose you put a narrowband filter on the sun (like pure red for example.) What will rainbows look like if the sun emits pure red light? A rainbow will then look like an extremely thin curved bright line, since only the “red band” of a normal rainbow would be visible.
However, if the raindrops are fairly small, you’ll also see something else as well. Below the primary rainbow (by “below” I mean inside the curve,) you will see a large number of parallel stripes. These are caused by the wave interference of light through the tiny raindrops. The stripes are called a “Fresnel Diffraction” pattern. The stripes closest to the main rainbow will be brightest, and the ones that are farther away are dimmer.
The secondary rainbow has these stripes too, but they appear “above” the secondary bow (outside the curve.) The primary and secondary rainbow together form the borders of a “dark slot”, with the opposite edges of the two rainbows having a lot of close-spaced parallel lines.
OK, now remove the red filter. What do we see? The main rainbow (the “bright line”) gets dispersed into spectral colors. Each frequency of light has it’s own “bright line” rainbow, and each rainbow has a slightly different position. But the set of parallel diffraction lines coming from each color frequency, those add and subtract strangely. Most of them blend to become the whitish mist below the main rainbow and above the secondary bow. But the very dark lines between those parallel lines add and subtract to create the “subtractive colors” seen in soap bubbles; colors such as magenta and cyan (green and purple.)
The cause of the green and purple in rainbows and in soap bubbles are similar: each spectral color is associated with a dark line, and when all the colors appear at once, the dark lines are spread out, and they form “negative rainbows” with subtractive colors. The “hole” in the red frequency creates cyan (cyan is everything EXCEPT red). The “hole” in the green freq. creates magenta (magenta is everything EXCEPT green). The “hole” in the blue frequency creates yellow. (Yellow is everything EXCEPT blue.)
I saw a rainbow of the type Chronos describes just the other day; there were at least two, possibly three extra green/blue/violet bands in there, but they were very tight compared to the main band. There was a secondary bow too.
OK, I had heard of the supernumary bows, but I had somehow gotten the impression that they were more or less colorless. Chalk it up to not paying attention at that colloquium, I suppose. In any event, I did at least get the experience of seeing one. (dangit, now I wish that rainbow smiley had won!)
Thanks, everyone! That’s a lot faster than I expected an answer!
CalMeacham, I would just like to say a sincere thank you for your excellent posts on rainbows. Almost a year ago I posted a thread on rainbows and you replied in a clear, accurate and articulate manner. I forgot to thank you at the time as I was still trying to get my head around it all. Since then, however, I have read(/battled with :)) some of the books you recommended and have managed to get a good handle on the subject. As a result, emailing a ‘thank you’ to you has been on my list of things to do for quite a while now but unfortunately I have never got around to it. This thread has jogged my memory.
Thank you for helping to illuminate the majesty of rainbows for me.
Obi Wan: Aw, shucks. (shuffles feet).
Just a couple of other notes:
1.) I suspect that part of the reason supernumerary bows aren’t always visible is that they require that the drops all be of nearly uniform size. If you have a broad distribution of drop sizes the bands wil have different widths, and will “wash out”.
2.) The alternating purple and blue-green color scheme of supernumerary rainbows is characteristic of multi-order white light interference. You see the same thing with soap bubbles and oil films. Unless these are very thin, their colors will be only purple and blue-green (and never red. Yellow and blue only show up if they’re very thin). If you want an explanation, see Boyer’s book in my above cite, or see C.V. Boys’ book on blowing Soap Bubbles (still in print from Dover). Or you can go to any optics book on color theory and crank through the math yourself.
3.) Yllaria – rainbows don’t circle the illuminating body in question. The primary rainbow is about 42 degrees from the anti-solar point (the point in the sky opposite the sun, which is obviously below the horizon, so you can’t get a complete circle unless you’re on a mountain or up in a plane). The same goes for the moon. Lunar rainbows do exist, and have been photographed, but from your descrioption, it sounds more as if you saw a lunar halo. See Minnaert’s book, or Tricker’s. Or Jearl D. Walker’s Flying Circus of Physics.
at the house where i used to live we would see the half circle rainbows quite often at least once or twice each year. we get lots of afternoon thundershowers here in the summer. we would usually see them kind of late in the afternoon, the sun getting low in the west and the rainbow would be in the east, we were in between. the terrain and lack of trees made seeing these rainbows a relatively common sight. on at least 3 occasions, i have seen the end of the rainbow touching the ground in my pasture. we once tried to drive up to one but as we approached, it moved away from us as our perspective of viewing changed. one time, i was sitting out on the porch and i was the end of the rainbow out in the pasture. i called my wife and children to come look. we were all out there watching and the end of the rainbow was moving straight toward us. it came across the field at about the speed of a fast walk. it came right up into my yard. it was a very strange, surreal sight. i took a photograph, but the photo looked more like a runny color development error. i still have the picture, but i dont have a scanner to post it. the photo was taken from a distance of 20-30 feet. the rainbow end progressed right up to us and disapeared as soon as it reached us. it was definitely an unforgettable sight. and for any of you wisecrack makers…no pot of gold.
(dangit, now I wish that rainbow smiley had won!)