Colour, prisms and rainbows

Crown glass bends violet light at 410 nm a little more than red light at 660 nm, because its index of refraction is 1.530 for violet and 1.512 for red.

White light is a mixture

In the mid-1660s Isaac Newton let a narrow beam of sunlight into a darkened room through a hole in the window shutter and passed it through a glass prism. A band of colours appeared on the far wall. In a paper published in 1672, which a 2015 commentary in the Royal Society journal Philosophical Transactions calls the foundation of modern optics, he argued that the colours are not added by the prism; white light is a mixture of them, and the prism separates them because each colour is refracted by a slightly different amount. He also showed that a single colour picked out from the band and sent through a second prism stays the same colour.

OpenStax explains the reason. For a given material the index of refraction depends slightly on wavelength: it increases as the wavelength decreases and is greatest for violet. Violet light is therefore bent more than red, and white light fans out into the familiar order from red to violet. Spreading white light into its spectrum this way is called dispersion. More generally, dispersion happens whenever a process changes the direction of light by an amount that depends on wavelength.

Colours and wavelengths

We usually name about six colours in a rainbow: red, orange, yellow, green, blue and violet, and sometimes indigo as well. OpenStax stresses that the spectrum is continuous: the names are labels for ranges of wavelength, from about 700 nm for red down to about 400 nm for violet. When the eye receives light of a single wavelength we tend to see one of these colours. The many other hues we can see are the eye’s response to mixtures. Sunlight contains all visible wavelengths and looks white, or very slightly yellow.

Objects get their colours from the light they send back to us. A leaf looks green under sunlight because it reflects more green light than other colours and absorbs much of the rest. Under a light that contains no green, the same leaf looks dark. A filter works in a similar way for light passing through it: a red filter lets red through and absorbs most other colours.

Rainbows

A rainbow is dispersion by water drops. OpenStax describes how light enters a drop, reflects from the back of it and leaves again, refracting both on the way in and on the way out. Since water’s index changes with wavelength, the colours leave at slightly different angles. You only see a rainbow when the Sun is behind you, and each colour reaches your eye from drops at its own angle from the direction of the sunlight, which is why the rainbow is an arc. Two reflections inside the drops make a fainter secondary rainbow above the first. Around 1300, as OpenStax tells, Kamal al-Din al-Farisi in Persia studied this with a large glass vessel of water inside a camera obscura, standing in for a giant raindrop, and Theodoric of Freiberg did similar experiments in Germany; both built on the work of Ibn al-Haytham.