PFE022: Rainbows

Rainbows are majestic, ethereal visions of color. While possibly (but not likely) not the most beautiful thing in nature, their intangibility has made them an object of interest throughout time. According to the Bible,

I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth.

Physicists tend to have a more down to earth discussion of the source of rainbows.

But first, I must explain the basis for many popular physicists jokes (yes we do, apparently, have a sense of humor). It is common in physics courses to work problems on a simple shape, say, a sphere, because the mathematics works out more easily. More complicated shapes usually follow in the same direction but with harder math (in practical applications this means computers), but the line "assume a sphere" is very common among physicists.

Anyways, rainbows form all the colors of rainbow by light passing through them. Yet this is different from both the mirage phenomena and the oil slick phenomena (I seem to like self-references, it holds things together?). The physics though is related.

First, consider white light. What we think of as white light is actually a collection of all (or nearly all) colors that we can see. We know this because we can pass it through a prism and it splits white light into all colors.

If you don't recognize this, shame on you.

From playing with prisms, we can see that light travels differently through glass depending on its color (remember oil slicks?).

When light travels through glass (or water) the light bends at the surface from air to glass (water) or vice versa. But how much it bends depends on the color (wavelength) of the light.

The next step is where we get to use our "sphere" approximation. Rainbows require airborne water droplets. These can come from sprinklers, ocean spray, or rain falling. In any case, the droplets may be any number of shapes that don't particularly resemble spheres. That said, for the sake of this exercise, suppose all the water droplets are spherical. Then, as white light enters the drop from the sun,

it bounces around inside the light and comes down towards our eyes. But as the light bounces around through the droplet, the colors eventually split into the rainbow spectrum.

This shot is a beautiful example of a double rainbow which is what happens when some of the light makes two internal bounces instead of just one as usual.

That's rainbows.