Colour vision and the colours of the rainbow

I’m working on a project that involves creating a number of images based on rainbows at the moment.
Here’s an example.

anglepoise lamp with rainbow
It’s a stylised image obviously, and one of those stylisations is that I’ve drawn the rainbow with sharply defined colours.
Rainbows don’t have sharply defined colours of course. Just look at the photo below for proof. The colours in the real rainbow move from one to another in infinitesimally small changes of hue. That’s because each colour is produced by a different wavelength of light. We can’t actually differentiate between all of those colours by seeing them as different hues, because our eyes just aren’t sensitive enough, but you can see quite a few of them.
When I say ‘see colours’, I really mean ‘create colours’, by the way – because light isn’t actually coloured at all, it’s just a wave of radiation or energy travelling through space: the colour is generated in our heads by our eye/brain partnership.

rainbow

How does the eye actually sees so many different colours?
The retina of the eye is covered with light sensitive receptors shaped like cones. There are three types of cone, each sensitive to a different range of wavelengths of light. One type of cone is sensitive to light of wavelengths that are towards the end of the spectrum that create the effect of blue to the eye, another type of cone is sensitive to light in the central area of the spectrum (that gives the effect of green), and the other is sensitive to light towards the end of the spectrum that gives the effect of red.
Importantly, each type of cone is sensitive to a range of wavelengths. If you look at the graph that I’ve drawn (below) you can see that, for instance, the cones that are sensitive to light that produces green are actually sensitive to light all the way from quite near the blue end of the spectrum to almost the red end.

cone sensitivity in the eye

The eye contains three types of cone, each sensitive to a different range of wavelengths of light

No matter which wavelength of light is hitting a cone, that cone only produces one colour sensation in your eye (or your brain, depending on how you want to think about it).
Sticking with the green cones as an example: the green cones are relatively sensitive to light near both the blue and the red ends of the spectrum (as you can see in the graph), but when light from, say, the blue end of the spectrum strikes the green cones it doesn’t produce the sensation of blue in the eye, it produces green. If you only had green cones in your eyes you’d see everything coloured green, even if the light was of a wavelength from the blue or red ends of the spectrum. Similarly, the blue cones only produces the sensation of blue when light strikes it, and the red cones produce the sensation of red.

So how do you see the colours in between the blue, green and red?
You see them because of the overlap in sensitivity between the different cones.
Take orange for example (see graph, above).
When light that’s at the wavelength that corresponds to the colour orange enters your eye it stimulates both the green cones and the red cones. It stimulates the red cones a lot more than it does the green cones, because the green cones’ sensitivity is dropping off towards the edge of their range – on my graph I’d say that the red cones are stimulated about three times as much as the green cones. The brain analyses the stimuli from the green cones and the red cones and produces a colour effect in the brain that is three parts red and one part green – in other words, orange.
The ratio to which the particular wavelength of light stimulates the different types of cone is the key to the creation of the different colours in the brain. For instance, on the graph you can see that there’s a spot near the top of the green and red cone curves where the curves cross. At this point the stimulation of both types of cone is exactly the same, which generates the colour yellow in the brain.

ROY G BIV – rainbow colours mnemonics
The colours of the rainbow tend to be listed as red, orange, yellow, green, blue, indigo and violet. Remembering the order of these colours is normally done by employing a mnemonic or aide mémoire, of which the two most common are:
Richard Of York Gave Battle In Vain and ROY G BIV (Why a nonsensical name like Roy G Biv works as a mnemonic I don’t know, but it does).
If you’re not keen on either of those, here are a few more rainbow mnemonics that I’ve just made up:
Rainbows Offer You Glorious But Illusive Visions
Rainbows Offer You Gold But It’s Vacuous (referring to the nonexistent pot of gold at the end of the rainbow).
Retire Once Your Gold Becomes Incredibly Valuable

Whichever mnemonic you choose, you’ve got seven colours.
That’s seven colours despite the fact that the colours of the rainbow are a smoothly changing continuum – not a seven step ladder.
The reason that the rainbow has been allotted only seven colours is historical rather than factual. The colours of the spectrum were first defined by Isaac Newton in the 17th century. He split the spectrum into seven colours purely for the purpose of mirroring the seven note scale of western music, with which he thought there was a parallel (or so I’m told).
There are several things that are a bit quirky about the colours that Newton chose to name (on top of the quirky reason why he chose to name seven of them). For one thing, they aren’t equally distributed along the spectrum, so there’s a bit of unnecessary bunching.
For another, he’s included the colour indigo, which is hardly a differentiable colour at all to the human eye – it could easily be dropped from the list without anyone noticing. When did you last describe something as being indigo? Never – that’s when. I’ve deliberately missed the colour indigo out of my stylised rainbow above, thus giving my rainbow a more manageable (but less mystical) six colours.
One of the other colours of Newton’s rainbow, orange, was only given its own name in the 16th century, the century before Newton listed it in the spectrum. Previously the colour between red and yellow was simply referred to as yellow-red (or perhaps red-yellow). One theory is that the colour got its name by being named after the well-known citrus fruit that is of a yellow-red (or perhaps red-yellow) hue – just as the colours violet and indigo were named after plants that exhibited those particular colours.
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