Reader Poll: The Optics Of Rainbows
Posted in Physics, Quickies, Science on | 1 minute | 4 Comments →
Today's post is just a quick one for the physics and optics students out there, who are welcomed to freely speculate. Actually, everyone is freely welcomed to speculate! Also, I'd really appreciate any links to people, websites or books that can provide useful information, so if anything comes to mind, by all means share!
I'm trying to get some kind of consensus on a recurring question I've got. We perceive rainbows because of a neat little process called chromatic dispersion by which white light refracts through water droplets in the atmosphere. The white light actually refracts twice: once upon entrance which separates the light into its constituent colors, and again upon exit which amplifies this separation. When a terrestrial observer sees a rainbow in Earth's atmosphere, what they're really seeing is the separation of incoming white sunlight into the familiar colors of the rainbow: red, orange, yellow, green, blue, indigo and violet.
My question is: if Earth were enveloped by a "shell" of solid water, would this affect the rainbow-creating process? Would terrestrial observers on Earth still be able to see rainbows?
Dominic Saltarelli
says...Tentatively, I’d say yes. Since the rainbow effect is caused by small spherical droplets, condensation below the firmament would still refract light that passed through the firmament the same as it does now.
D
says...Wait, wait, wait… are we talking about the ice shield here? Because I think you basically asked about an ice shield. Is the idea that we had the ice shield before the Noachian flood, so there were no rainbows; but the flood used up the ice shield, and how we have rainbows and are able to land on the moon? Is that where this is going? Just checking.
As for your actual question, let me posit two extreme scenarios and show what I think would happen.
If the ice is a basically smooth, hollow, spherical shell, then this will act as more or less a giant lens as the dome will focus all the Sun’s rays to whatever spot on the planet is experiencing “true noon” (where the Sun is directly overhead). To put it mildly, such a phenomenon would leave clear and unambiguous effects on the face of the planet. All the incoherent light striking the dome would still be differentially refracted through the shield based on wavelength, though – but this would manifest as a “circular rainbow” surrounding the Sun as a consequence of chromatic aberration (how it works, what it looks like). We get a little of this even now because of atmospheric diffraction (the sky’s “blue-ness” is a direct consequence of light leaving one medium and travelling into another). However, unless an observer is looking up at the Sun/lens, light as viewed by an observer on the surface will still be more or less incoherent, and I suspect there would still be rainbows – they would just be relative to local light content, which in its turn would depend on the geographical relationships between observer, mist cloud, and “true noon.” Rainbows would be different, in other words, but not absent (I think). Near the geographic poles (those points opposite each other on the Earth’s circumference, describing a line parallel to the plane of Earth’s orbit ’round our star), there would probably be some total internal reflection occurring, which could have the interesting consequence of making the ice shield glitter on the night side (but this would be invisible during the day), which I think would look really neat.
At the opposite end of the spectrum, so to speak, the ice shield could also be frozen particles swirling in geostationary orbit. Particles at the poles would have problems, maybe it would be more like an ice sleeve or something. But now we’ve got incoherent light passing through what is essentially a randomized and constantly-shifting set of tiny lenses/mirrors (depending on how light strikes a particular bit of ice), and it’s “garbage in, garbage out” from there. The view from Earth would be basically unchanged, though perhaps there might be a cool-looking rainbow at the horizon at noon every day.
In between, we’d get something in between. A blocky, solid shell would probably produce local foci for the incoming light while leaving sunlight basically unchanged for interior observers, and the larger the particles get in a particulate shield, the more it would look like this, too. But rainbows are a necessary physical consequence of imperfectly organized light moving from one medium into another (you can even see them through windows or prisms), so I don’t think an ice shield would get rid of them, so not even the ice shield makes the Noachian covenant a real explanation for rainbows as such.
Karla
says...Wouldn’t you have to have rain to have a rainbow? The sun reflects on the rain creating a rainbow, right? So if water enveloped the earth without producing rain there would be no rainbow. . .
D
says...Karla, not quite. I just pored over the Wikipedia page on rainbows, and I’m starting to doubt even my own suppositions from above. Bottom line: hmm… now I’m not so sure.