I recently saw a scene on TV which, obviously faked, had a rainbow over a sea-loch in Scotland with a mirror image of said rainbow reflected in the still waters of the loch. This led me to speculate on whether or not a rainbow would have a reflection at all. After all, the rainbow is not actually ‘there’, it is an optical phenomena which gives the illusion of being up in the sky. Does anybody have the straight dope on this?
I’ve seen a genuine photo of a rainbow with a ‘reflection’ in a lake. It’s actually a refraction - if you’re at the right elevation above the water surface, the angles work out correctly to see a second rainbow.
Here in Hawaii, where we are resplendent with rainbows, rainbows do 
indeed reflect off of other things. Its just a question of angles. 
I happen have the San Francisco Bay immediately to the east of my office. Yes, under the right circumstances, you can see the rainbow and its reflection in the water form a full ovoid.
For that matter, you can see a rainbow in a mirror too. If the reflection seems poor when it comes from a lake, that’s only because water is a weak reflector.
At the risk of provoking Gorillaman’s ire, it isn’t refraction at all, just normal reflection.
A reflection isn’t actually “there” either … it’s just an optical phenomenon. There’s no reason for light rays which have been refracted in raindrops to behave any differently than light rays which have bounced off solid objects when they encounter a reflective surface.
Technically, yes. But the key point is that (unlike a physical object) a rainbow is only visible to people standing on one side of it. For example, if there was a giant mirror BEHIND the rainbow, you wouldn’t see the rainbow reflected in THAT.
The reflection only occurs if the reflector is roughly within the same viewing angle as you are. Position the reflector too far off your viewing axis and the reflection will distort or disappear entirely.
No ire 
…obviously, straightforward reflections are possible. Maybe I misphrased my earlier post - in some cases it’s a refraction. The one I’m thinking of had the two arcs at completely different orientations.
But isn’t it true that rainbows don’t reflect off Loch Ness? They have a similar anomally there with duck vocalizations as well, so I’ve been told.
Inigo:
To the OP: sure it’d reflect. There’s no reason for it not to. If you took a boat to where you saw the reflection, you’d see the rainbow in the sky.
There’s one factor that might reduce the visibility of parts of the arc. The rainbow is partially polarized tangential to the arc. Any transparent surface will partially polarize light reflected at the correct angle and filter rather than reflect polarized light coming at it. Therefore at the correct angle parts of the arc could be fainter than the rest.
There’s another thing that can happen with rainbows and bodies of water: Just as the Sun can cast a rainbow, so too can a reflection of the Sun. If this happens, instead of just having an arc of a single circle, you can have arcs of two different circles, which intersect at the waterline. Of the rainbows above the water, in the sky, the regular one will be less than a half circle, while the one from the reflection of the Sun would be more than a half circle. If reflections of the rainbows were visible, then you’d see two complete circles, part above the horizon, and part below.
A thought, meanwhile: It’s probably uncommon to see reflections of rainbows in water, since the water beneath a rainbow is getting rained upon. So at least part of your body of water, and possibly all of it, is going to be choppy, and therefore won’t reflect well.
I was coming to say what Chronos said, but I may as well add that I posted a picture of the latter phenomenon on the SDMB a while back - a normal rainbow plus a rainbow caused by a reflection of the sun in the sea.
Hmm, I can’t find the thread in question, but someone suggested I submit the photo to the Earth Science Picture of the Day site, which I did, and you can see it here.
Vampire rainbows don’t have reflections; the other kind do.
…The chief difference of course being that the gold is found in a casket, as opposed to the conventional crock.
I saw one of these a couple of months ago just before sunset. In fact, there was a double normal rainbow in addition to a rainbow due to reflection from San Francisco Bay.
Just a nitpick:
Chronos says:
The water underneath isn’t necessarily getting rained on – a rainbow is formed when you have a lot of spherical droplets at a point in the air where your line of sight to them is 42 degrees from the line of sight to the anti-solar point (the point opposite where the sun is. Generally underground when the sun is up, unless you’re on a mountain or in an airplane). Therefore the droplets could be very far away, but not over a lake that’s much closer to you. Therefore the rain wouldn’t be over the lake. Besides that, light rain probably wouldn’t mess up the surface of the water enough to spoil a reflection, anyway.
One interesting twist is that, since the effective line of sight for a reflected rainbow is different than that for the “original” rainbow, the resulting rainbow won’t seem to be in the same place relative to the rest of the reflection in the lake. See the drawing in Jearl Walker’s The Flying Circus of Physics.
By the way, as rowrbazzle notes, the rainbow is polarized. But , while it’s correct to say that it’s partially polarized, it’s actually very nearly completely polarized. I took to carrying pieces of polaroid polarizer in my wallet when I lived in SLC (where there are a lot of rainbows – even if no “natural” ones form, everyone waters their lawn twice a day) just to see the effect, which is pretty dramatic. Just for the record, though, you don’t see extinction from this effect in any of the photos I have of reflected rainbows. You need to have the viewing angle close to Brewster’s angle for that to occur.
For more on the topic, see M. Minnaert’s classic The Physics of Light and Color in the Open Air, Greenler’s book Rainbows, Halos, and Glories, or R.a.R. Tricker’s Introduction to Meteorological Optics
IIRC, there’s a phenomenon where the refraction occurs “twice”*, resulting in a second rainbow, with its colors reversed.
*Probably not the correct term, but cut me some slack here.
Close, but no rainbow cigar.
A Secondary Rainbow occurs when there are two internal reflections within the raindrop (there are two refractions, as with the primary rainbow – one for rays entering the drop, one for them leaving). This does indeed result in a rainbow at about 54 degrees or so, with the color ordering reversed. It’s also lower in intensity, since light has already leaked out at the first internal reflection (not all the light gets reflected).
There are higher order rainbows, with larger numbers of bounces – tertiary, quaternary, etc. You don’t see tertiary and quarternary rainbows in nature because they would be awfully close to the sun and they’re very weak. (See the references I cite above, and the references cited i them. Jearl Walker himself published a gorgeous paper in, I think, the American Journal of Physics that showed the first 20 or so orders of rainbows, their widths, and positions, in full color)
The first tertiary rainbow was seen in a “laboratory” in the 14th century by a couple of Persian opticists, al Shirazi and his student. They used a spherical glass flask full of water as a model raindrop. About twenty years later Theodoric of Freibourg did the same experiments in France, but I don’t think he saw a tertiary rainbow. He did see and draw primary and secondary rainbows. But his work, as well as that of al Farisi and al Shirazi, was forgotten, and it as left for Descartes and Newton to re-discover. See Boyer’s excellent book The Rainbow: From Myth to Mathematics