When you see three rainbows close to each other in the sky, the third one isn’t a tertiary rainbow – the tertiary is too far away from the first two.
One situation which can cause an apparent tertiary rainbow near the primary and secondary is when you have, in addition to the regular primary and secondary, a third “primary” rainbow due to the reflected image of the sun, bouncing off a lake or mirror-sided building behind you, or even (if the sun is low enough) reflection off the ground. It’s not a common phenomenon, but it ,must be more common than observation of a true tertiary.
Another possibility is that you saw a supernumerary rainbow. Physical Optics theory of the rainbow indicates that you reallu ought to get multiple rainbows from single drops, and these have been easily observed in the laboratory, especially with laser light. In nature they tend to get washed out by the resence of raindrops of multiple sizes, but they have been observed – I’ve seen them myself, and they’ve been photographed. Not nearly as rare as the other phenomena mentioned in this thread.
There may be other situations that produce such a third rainbow. Meteorological Optics is a still-developing field, despite being over two centuries old.
Hm. There were no lakes or mirrored buildings around–we were in a 70’s era neighborhood of apartments, houses, and stores–and it was about 4:00 or so in the afternoon, I think. The sun was lowish but not incredibly low. It was in April. So maybe a ground reflection?
Supernumerary rainbows are the extra bands of color right under a rainbow, right? We see those every so often. This was 3 separate rainbows, your usual double with a third even fainter one above that, fairly high above but not on the other side of the sky. I can’t explain it, and I’m not sure if I have pictures. If I do they’re on film, not digital, but rainbows photograph so badly IME that we may not have tried; we probably just stared.
Right. Supernumerararies tend to go aqua-pink-aqua-pink-etc. below the violet part of the primary bow, and are classic cases of colors due to multiple order white light interference.
If you saw this extra bow above the other two (a secondary is above the primary, with colors reversed), then that strengthens the case for a primary bow due to a reflected sun – that’s where those appear. It ought to have colors in the same order as the primary, with red on the outside (top).