DURING this crisis, people have been putting pictures of rainbows in the windows of their houses and online. Rainbows have an unrivalled dominance in the history of hope symbols.

They have been used all over the world in the service of a vast range of causes.

In modern life, not just for religious causes and LGBT liberation, the “PACE” (peace) flag against the Iraq war, the Wiphala flag of South American indigenous peoples (including Evo Morales supporters in Bolivia) are all rainbows.

The International Cooperative Alliance also used a rainbow flag from its inception in 1925 until 2001. Further back, a rainbow flag was used as an emblem by the uprising of peasants and farmers in the German peasant war of 1525.

The unexpected beauty of rainbows is a potent symbol for unity in diversity.

Rainbows have naturally inspired a huge amount of scientific curiosity throughout history. Aristotle had influential ideas succeeded by Ibn al-Haytham’s principles of optics.

Scientists of the Islamic Golden Age devoted lots of attention to them, and by the 13th century both Kamal al-Din al-Farisi and Roger Bacon had a good understanding of how rainbows worked.

They knew that a rainbow effect could be produced by using a round glass bottle of water as a huge model raindrop. By using a small hole in a screen which blocks most of the sunlight, a rainbow arc can be seen reflected back onto the screen.

These scientists were able to explain the colours, shapes and arrangements of rainbows using just the geometry of spheres, reflection and refraction (the way light bends as it passes from one material into another).

However, perhaps the most influential work on the way we imagine rainbows was done by Isaac Newton.

He carried it out while he too was isolated in lockdown, during the bubonic plague of 1666. Using the same idea of a screen with a hole in it, Newton considered the splitting of a beam of sunlight by a triangular prism (instead of a spherical bottle) into its many colours.

Although this had been observed before, he showed that the colours could not be split further, but could be recombined to form white light.

Strongly contested at the time, the idea of the plurality and distinctness of colours and the unity of their combination in white light was bolstered by Newton’s description.

Newton also popularised the idea that there are seven discrete colours in the rainbow — (medieval observers had generally counted four, like the elements) which he favoured because of a belief in the mystical properties in the number.

Newton’s theory used particles moving in straight lines. It’s this “billiard-ball” movement that you can imagine as light enters a spherical droplet, bounces off the back surface and exits out of the front again at a different angle.

Each colour is bent slightly differently on entry and exit of the droplet, splitting up the light as through a prism.

The idea of “unweaving the rainbow,” a phrase borrowed from Keats, has been used to denote a loss of magic in a scientific worldview. Scientific narratives are indeed culturally powerful.

Newton’s idea that light was made of particles was so widely accepted in the 18th century that even poets who hated science, like William Blake, made extensive use of the image in his poetry as he explicitly railed against the scientists who had invented it.

However, these influences change as the theories do. The earlier theory worked well for the ROYGBIV rainbow and could even account for the double rainbow — a second, much bigger arc with the colours in the opposite order.

But it couldn’t explain “supernumerary” rainbows: extra pink and green stripes on the inner violet edge of the rainbow which don’t fit neatly into our idea of a standard rainbow.

These extra colours are caused by the way light waves interact with each other and the raindrop. They depend strongly on the shape and size of the raindrops they come from — you can’t observe them using a big round bottle, so they had previously been ignored.

In order to understand these “interference” colours it took a description of light as a wave. Many other variations in the shape and colour of rainbows are also caused by the size of the raindrop — different rainbows really do look different.

However, it seems like our mental image of the rainbow is taking a while to catch up.

While the recent sunny weather might mean that pictures are all you’ve seen of rainbows during the pandemic, there are lots of other rainbow phenomena you might spot.

Several phenomena are produced by the tiny ice crystals of that form in high cirrus clouds all year.

The most common of these effects are sun dogs — lumps of rainbow either side of the sun, about one handspan from it if you stretch out your arm, occasionally accompanied by a white circle halo connecting the two sun dogs around the sun or moon.

In cloudy weather, you might spot a “corona,” a small pastel-coloured ring around the edge of the sun or moon. The effect is visible when the intensity of the sun is reduced by a cloud or more commonly around the moon.

A similarly small ring can be seen around the shadow of your head if you turn away from the sun called a “glory.”

To see it you need to be looking down into clouds, so it’s not often seen except in mountain fog (or around the shadow of a flying plane).

You might be able to spot your own 21st-century glory by holding a laptop or phone screen in front of you with your back to the sun.

When your head and the sun are perfectly aligned with the screen, you might be able to see brilliant rings of colour reflected in the screen around the shadow of your head.

The colours you can see from plate-glass gadgets come from the thin layers of plastics and glass and the arrays of tiny pixels inside the screen.

Although the way that light reflects and refracts from the surface is very different from in raindrops, we need the same description of light as a wave that helps us see all the colours of a true rainbow, and the same geometrical ideas generated by the scientists who first considered the rainbow.

Children’s rainbows with their diversity of colour schemes may be truer to life than the ideal seven-colour rainbow that we learnt from Newton.

Rainbows are an incredible phenomenon, each unique to every individual but shared by everyone. They are a worthy symbol of our collective hope.