« What Kind of Message Is That? | Main | Big Biker Daddy »


A series of evening squalls have taken the pollen out of the air.

On the way home from dinner at a local restaurant we spotted a spectacular rainbow, visible along its entire arc once we found a good vantage point. There was a second, containing bow as well, its spectra ordered opposite to its companion. The brighter inner rainbow had a property I don't remember ever noticing before: at its inner limit (after violet) there were two additional spectra, closely packed and dominated by their own violet components, as if the rainbow has two small children clutching at its hems*.

This was the first rainbow our son has seen. I stopped the car, took him out of his seat, and pointed out the spectacle. I can't say for certain that he spotted the rainbow but he raised his hand alongside mine and pointed with me. He's only one, and everything is new.

As I started writing this the birds in the trees around our home were going bonkers, a sunset ritual this past week. They're calming down again now but I still hear one or two of them wooing for all he's worth.

* Addendum: I've done some research. Read on:

I pulled out my prized copy of Atomospheric Phenomena (W.H. Freeman and Company, 1980), a collection of Scientific American articles from 1949–1980. Chapter 7, "The Theory of the Rainbow," was written by H. Moysés Nussenzveig and originally published in April 1977. It describes the apparaition of the rainbow as follows:

The single bright arc seen after a rain shower or in the spray of a waterfall is the primary rainbow. Certainly its most conspicuous feature is its splash of colors. These vary a good deal in brightness and distinctness, but they always follow the same sequence: violet is innermost, blending gradually with various shades of blue, green, yellow and orange, with red outermost.

Other features of the rainbow are fainter and indeed are not always present. Higher in the sky than the primary bow is the secondary one, in which the colors appear in reverse order, with red innermost and violet outermost. Careful observation reveals that the region between the two bows is considerably darker than the surrounding sky. Even when the secondary bow is not discernable, the primary bow can be seen to have a "lighted side" and a "dark side." The dark region has been given the name Alexander's dark band, after the Greek philosopher Alexander of Aphrodisias, who first described it in about A.D. 200.

Another feature that is only sometimes seen is a series of faint bands, usually pink and green alternately, on the inner side of the primary bow. (Even more rarely they may appear on the outer side of the secondary bow.) These "supernumerary arcs" are usually seen most clearly near the top of the bow. They are anything but conspicuous, but they have had a major influence on the development of theories of the rainbow.

[emphasis mine]

I love the name "supernumerary arcs," even if it is perhaps a little unromantic. "Alexander's dark band" is a great name too. I'm happy to have seen the former (and probably the latter as well, although I can't claim to have noticed it).

2nd Addendum: supernumerary arcs can be seen here. I found that link at the Wikipedia, which, no surprise, has excellent information on rainbows, with bibliographics references to the usual suspects: Minnaert, Greener, Livingston, and Lynch, the last of whom wrote the preface to the volume I referred to above.


We saw the same rainbow!!!! Washing up our dinner dishes I glanced out the window and there it was. We raced outside to get a better view. Wow!

I've added the footnote/"MORE..." content above with the results of some research into what we saw. Atmospheric Phenomena does not appear to specify the area of visibility of a rainbow (or at least I cannot find such an explanation) so I cannot for the moment confirm whether we may have seen the same one. I suspect they were each our own rainbows, produced by our shared weather pattern, since we're something like 200 miles / 300km apart. I'll add more here if I can find an answer.

OK, I haven't found a straight answer but I've essentially compiled one. First remember that rainbows are composed of light deflected within water droplets in rain-producing (nimbus) clouds. Each drop produces its own rainbow, the cumulative effect being the sum of all of these. For this reason the same rainbow cannot be glimpsed from two vantage points no matter how close. But that's a bit of a pedantic interpretation of "the same rainbow". In the spirit in which you wrote I think we could be said to have seen the same rainbow if we saw a rainbow produced by the same cloud(s), so the question becomes one of the area of visibility of a raincloud.

Cumulonimbus clouds can be quite low but they can also range up to about 50,000 feet (2,400m). We saw the rainbow in your general direction, to the northeast (it was almost sunset with the sun low behind us in the southwest). In principle if the cloud could see us both then we could both see the cloud. Thus we must ask how far the horizon is from an altitude of 50,000 feet.

The horizon distance in km is the square root of 13 times the viewer's elevation in meters. 50,000 feet, as mentioned above, is about 2,400 meters, so we take the square root of 13 x 2,400 (= 31,200) and get 177km (110 miles). Thus a cloud at 50,000 feet could "see" points on land up to 110 miles away in any direction, and could have both of our homes in sight if the cloud was floating over a point roughly midway between us, since we're less than 220 miles apart.

This, however, does not mean that we could both see rainbows produced by the cloud, and in fact it effective shows that we couldn't. The reason for this is that in the case of our particular two locations the cloud would really have to be halfway between us, placing it to the northeast from here but to the southwest from your home. And a cloud in your southwest is in the wrong place to make a rainbow from your perspective.

Really though we're not talking about a single cloud but all the water droplets involved in producing a rainbow, so if we think of these droplets as being produced by a large bank of water vapor (in one very broad cloud or a large group of clouds blown on the same wind) then I guess we could say our rainbows were from the same storm, and in that sense the same. Certainly the prevailing weather is closely related for our two locations and the characteristics of the current cloud/storm system are likely the same.

This has all been interesting for me to ponder but looking back on the process here it's all highly pedantic and likely pretty uninteresting for you, for which I apologize.

I can't speak to the theory of rainbows, but I absolutely love the name H. Moysés Nussenzveig -- at first I thought there might be a typo in there (there are several in your post, I fear), but I found his website and sure enough, it's a fine Judeo-Brazilian name.

The rainbow was gorgeous!

Oof! Typos! Some of them were pretty funny but I think I've taken care of them now. I would blame sloppy fingers and the lateness of the hour but in honesty I didn't proof-read it. I generally do take greater care when inserting less familiar characters such as those in Nussenzveig's name.

By the way, when I reread the post just now I noticed that in the footnote I added where I quote Nussensveig his description seems to suggest that the phrase supernumerary arcs refers just to those visible outside the secondary rainbow, but the illustrations in his article most definitely imply that this name is also used for the less uncommon arcs which occur inside the primary rainbow.

I forgot to tell you how much I loved this poetic image of yours:

"...as if the rainbow has two small children clutching at its hems."

Post a comment

(If you haven't left a comment here before, you may need to be approved by the site owner before your comment will appear. Until then, it won't appear on the entry. Thanks for waiting.)