Forty-Two And The Rainbow
A rainbow never fails to enchant, a transient moment of celestial beauty, even though it is one the commonest of meteorological phenomena. For Keats it was enough to admire it for what it is, railing against Isaac Newton in 1817 for destroying “the poetry of the rainbow” by “reducing it to a prism” and, in Lamia (1820), lamenting that scientists “will… conquer all mysteries by rule and line/ empty the haunted air and gnomed mine/ unweave a rainbow”.
The first step on the yellow brick road to understanding rainbows was taken in 1621 when Dutch scientist Willobrord Snell developed his law of refraction. Discovering that when light travels from one medium to another, for example from air to water, it generally bends or refracts, he was able to calculate the degree of bend.
René Descartes then created a rainbow in his laboratory by passing light through a flask of water and applied Snell’s law to calculate the angles of refraction and reflection of a beam inside a droplet of water. He documented his findings in the first detailed study of rainbows, L’arc de ciel, later to be incorporated into his Discours sur la méthode (1637). One thing baffled him; why was a rainbow made up of different colours?
Isaac Newton answered that in Opticks (1704). Passing light through a prism, he found that it decomposed into seven colours and that the order in which they appeared, red orange, yellow, green, blue, indigo, and violet, immortalised in the mnemonic Richard of York Gave Battle In Vain, remained the same every time.
There is some debate as to whether indigo, for many indistinguishable between blue and purple, should be a separate colour in the rainbow spectrum. Was Newton, more romantic than Keats gave him credit for, lured by the by the cosmic significance of the number seven? It is more likely, though, that in Newton’s time the distinction between indigo and blue was more marked, blue being more of a greenish-blue aqua-like colour compared with the bolder hue of indigo, one of the most valued and expensive dyes of the age.
In the world of rainbows, though, seven pales into insignificance compared with forty-two, the answer to the ultimate question of life, the universe, and everything, according to Douglas Adams’ The Hitchhiker’s Guide to the Galaxy (1979).
On meeting a droplet of water, some rays of light will penetrate it, and are refracted on the way in, reflected as they hit the back of the drop, and refracted once more as they leave. The rays hit the drop at various angles, and the higher up they strike, the greater the angle of reflection. The most intense concentration of light, the Descartes ray, occurs when the rays are reflected at around forty-two degrees. It is at this point that the raindrop scatters most light, producing the bright and vibrant colours that form a rainbow.
When the white light decomposes into its distinctive colours, their order is determined by the wavelength associated with that colour. As the colour’s wavelength does not change, the order in which they appear in a rainbow remains constant. Blue, with the shortest wavelength, is refracted at a greater angle than red, the colour with the longest wavelength, but after the rays are reflected from the back of the droplet, the angle at which the blue light exits is slightly smaller than that of the red. As a result, blue is seen on the inside of the rainbow’s arc and red on the outside.
