I’ve seen this phenomenon first hand a couple of times. This one time, the second rainbow was almost as bright as the first one and the entire scene was really beautiful. However, you could also just make out a third rainbow outside the second one, colors reversed once more (ie the same as the innermost rainbow), flickering in and out of existence. It was never there for more than a second or so, but kept coming back. It was always very faint, nowhere near the brightness of the first two.
Is this because light sometimes bounces around thrice inside the droplets and exits at an angle of ~60 degrees? Are there any documented cases of quadruple rainbows?
The light can bounce around any number of times, in principle, but the more bounces you’re asking for, the less photons will do so. So the higher order rainbows are always fainter. I think I recall reading of laboratory measurements of something like 15 bounces inside a droplet, but that wasn’t exactly a real “rainbow” (which depends on the viewer seeing light from many droplets in different places), nor was it exactly “seen”. I’ve never heard of fourth-order rainbows “in the wild”, and even third order ones seem to be quite rare. Count yourself very lucky to have seen one.
I believe that there’s a Staff Report in the works for this one, but it’ll have to wait at least until Lynn gets back on her feet.
MY wife and I were coming through Colorado in the Summer of 1981, at least that’s where I remember us being. We saw a three banger. Couldn’t believe it. The planets must have been aligned. While the third one was far weaker, I was surprised that it was stable and clear. The second one was almost as strong as the first, as Priceguy experienced.
A good reference on rainbows is Jearl D. Walker, American Journal of Physics, Vol 44, pp. 421-433 (1976). He actually observed a 17th order rainbow in corn syrup in the laboratory.
Ninas grandpa is right that the 3rd order rainbow is supposed to appear back toward the sun…in particular, about 38 degrees (blue) to 42.5 degrees (red) away from the sun. [By contrast, the 1st order rainblow is 40-42 degrees away from the direction opposite the sun. So, what the OP describes here cannot be a 3rd order rainbow. In fact, it is hard to see how it could be any of the lower orders. So, my guess is it might have been something else. For example, one can get more complicated effects if some of the refraction is off of ice crystals rather than water droplets. Or maybe it has to do with some effect due to nonsphericity of the droplets. And, then there are effects due to the wave nature of the light (which is basically ignored in the geometric optics calculation of rainbows). I would have to say it is a mystery to me at this point.
By the way, I noticed that Cecil’s whole answer on rainbows was a bit simplistic in that it seems to imply that all the light that bounces once inside a raindrop exits at an angle of around 40 degrees. That is not so. In fact, this light exits at a variety of angles between 0 and 40 degrees. 40 degrees happens to be a “turning point”, i.e., a maximum value for the light to exit so a particularly large amount of light exits around that angle. (This is analogous to the fact that if you throw a ball up in the air, it spends more time at a height within, say, an inch of the top of the arch than it does at any other height…because it is almost sitting still there.)
This phenomenon of turning points leading to bright rings of light in optics is quite ubiquitous and the bright rings are called “caustics”. A rainbow is then a caustic that is colored by virtue of the fact that the ring occurs at a slightly different place for the different colors of light (because of the phenomenon of “dispersion” whereby different colors of light bend [“refract”] different amounts upon entering the water from the air and vice versa).
Here is a webpage on rainbows. Here is a site that shows the “supernumerary rainbows” that can’t be accounted for by geometric optics. Also note that the 2nd picture in particular shows very clearly how the sky is brighter inside the first primary bow. The reason for this is my above statement that light rays that reflect once inside the raindrop emerge at angles of 0 to 40-ish degrees but not at angles any greater than that. Hence, the sky inside is brighter due to that light that has reflected once. Light that reflects twice and forms the secondary bow emerges only at angles greater than 50 degrees and hence it is claimed that there is a dark band between the two rainbows although I have never been able to observe this…It certainly isn’t obvious to me in these pictures that it is any brighter outside the 2nd bow than it is between the two bows.
Wish I’d seen this earlier. jshgoe is quite right about tertiary rainbows – they’re in the direction toward the sun, as are quaternary rainbows. The tertiary rainbow was first seen by a couple of Persian scientists – al Farisi and al Shirazi – around 1300. But they saw it “in the laboratory”, not in nature. They quite properly noted that it was “very faint”. See C.B. Boyer’s The Rainbow: From Myth to Mathematics.
One possibility for a “third rainbow” is that you could be seeing an ordinary primary and secondary ainbow, along with a portion of a “reflected rainbow” due to light from an image of the sun reflected in a pond. (see Jearl Walker’s book – ot the above-cited article – The Flying Circus of Physcs, or R.A.R. Tricker’s excellent Introduction to Meteorological Physics, which has the best intro to the math of rainbows) This “refleced rainbow” is the source of reports of "rainbow pillars"and other unexpected phenomena. So it may not have been the planets that were in proper alignment, but you, the sun, and a convenient lake.