(* Warning — Some readers may find this massively pedantic *)
A while ago I did some research into rainbows. I’d been reading about Newton and his rings, and thinking about what people say about him and his opinion on the number of colours in a rainbow. In which way these “principal colours” were important to him is a little unclear (“because they pass into one another by insensible gradation” !?!!?!, link), but it seems to me that he understood the relation between the continua of pitch and hue and their (somewhat arbitrary) relation to the respective discrete scales rather well. Anyway, I thought I would have a go at asking how many colours there are in a rainbow, perhaps there would be a sensible answer… I gave up pretty quickly, because I noticed something else.
The first thing I did was get a prism, and have a look at what it does to the light. Well actually the first thing I did was write a computer program that simulated it, then I actually got a real prism (guess that says something about me). “Hang on, That’s not right!” I thought. Naively, I expected to see a rainbow, but I didn’t!!!!! I saw a spectrum for sure, but I didn’t see a rainbow. This is the sort of thing you see (of course its a (probably enhanced) photo):
(taken by D-Kuru/Wikimedia Commons)
And a rainbow, in comparison, looks more like this:
They really are quite different, In particular, notice the turquoise, violet and multiple bands in the second one. The huge amount of blue in the first.
So I thought I would simulate an compare them. Here are the results plotted as a line in the CIE u* v* colour space. For the prism I have used Monte Carlo (a got bored waiting hence the wibbly) rays from a slit traced onto a planar screen. I assumed Sellmeier type dispersion for BK7 glass. For the rainbow I used 0.1nm resolution Mie scattering simulations of 300micron water droplets (refractive index data from “The International Association for the Properties of Water and Steam” (link)… I love that such an institution exists). I have only plotted the part of the rainbow on the inside of Alexanders dark band.
Thing thing to note here is how the graphs look absolutely nothing like each other. The source of the difference is in the added wave interference effect (not a technical term) found in the interaction of light with the tiny little water droplets (Kat, if you’re reading this, another example of how big things are different to small things).
The majority of my colleagues I have mentioned this to have been quite surprised, philosophers and physicists alike. I started to think that actually, most people think a prism makes a rainbow – despite the fact that they look completely different. I would guess that pretty much everyone in the developed world has at some point in their lives performed the experiment in the first picture. Has no one ever noticed this? perhaps the ones who do notice the difference have it beaten out of them in the playground (or by their teacher). I hadn’t noticed, even though I knew the physics behind the two phenomena are different.
I investigated further. A search on google for prism yields a whole bunch of depictions of dispersion, many of which have been manipulated to make it look like the prism produces the correct colours for a rainbow (draw what you know, not what you see). CONSPIRACY!!!! It goes quite deep: a quote from the Wikipedia page on prisms: “A prism can be used to break light up into its constituent spectral colors (the colors of the rainbow)”. refractive index: “[…] and it is what causes a prism to divide white light into its constituent spectral colors, explains rainbows”… and so on, The myth is perpetuated…
The science behind what I’m presenting here isn’t unknown, in fact, it is very well established. I mention it only because I am fascinated by the extent of the conflation. Obviously, it doesn’t effect many peoples lives in any practical way. But on the other hand, rainbows get a disproportionate amount of attention. They’re a notable battleground in the conflict between art and science. Yet somehow there is this wide misunderstanding. Most likely it comes from (incorrectly) using rainbows as examples of dispersion in schools.
More info about atmospheric optics, All code available on request.