Rainbow

A rainbow is an optical phenomenon that appears in the sky. It forms when refraction, internal reflection and dispersion of light take place in water droplets. These processes spread light out into a continuous spectrum of colours, which appears as a multicoloured circular arc. Rainbows caused by sunlight always appear in the part of the sky directly opposite the sun.

Rainbows can form from many kinds of water in the air. They are not only caused by rain, but also by mist, spray, and airborne dew.

When seen from the ground, a rainbow usually looks like a glowing arc. When flying, however, a rainbow can appear as a full circle if there is enough mist. The centre of the curve is always on a line from the Sun to the observer's eye.

In a primary rainbow, red is on the outer edge of the arc and violet is on the inner side. A double rainbow has a second arc about 10° outside the first. Its colours appear in reverse order, with red on the lower side of the arc.

The Guinness World Records holder for the longest-lasting rainbow observed lasted 8 hours and 58 minutes. It was seen in the Yangmingshan range of Taipei, Taiwan, in November 2017.

Visibility

Rainbows can be seen whenever there are water drops in the air and sunlight shines from behind you at a low altitude angle. This is why rainbows are usually seen in the western sky in the morning and in the eastern sky in the early evening. The best rainbows appear when part of the sky is still dark with rain clouds and you stand where the sky is clear in the direction of the Sun. A larger but fainter secondary rainbow is often visible too. Rainbows are also commonly seen near waterfalls or fountains. Rarely, a moonbow, or lunar rainbow, can be seen on bright moonlit nights. Because visual perception of colour is poor in low light, moonbows often look white.

Photographing the whole rainbow in one picture is hard, since it would need an angle of view of 84°. With a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be needed. Now, software for stitching several images into a panorama can join overlapping photos to show the full arc. From above the Earth, such as from an aeroplane, it is sometimes possible to see a rainbow as a full circle. This can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°. Light from a primary rainbow arc is 96% polarised tangential to the arc.

Number of colours in a spectrum or a rainbow

See also: Spectral color

Isaac Newton first divided the spectrum into five main colours in 1672: red, yellow, green, blue and violet. Later, he added orange and indigo, making seven colours, like the number of notes in a musical scale. His choice was partly based on ideas from ancient Greek sophists, who linked colours, musical notes, the Solar System and the days of the week. Today, many people remember the seven colours with the mnemonic Richard Of York Gave Battle In Vain, or with the name of a made-up person, Roy G. Biv. A more modern list is red, orange, yellow, green, cyan, blue and violet.

A rainbow's colours look less bright than those in a spectrum, and the number of colour bands can change depending on the size of the water droplets. Rainbows also have bands of light beyond red and violet, in the infrared and ultraviolet regions, but people cannot see these. Water and air become opaque to these light frequencies, so only the ones close to visible light appear in rainbows. Whether everyone sees seven colours is a question connected to linguistic relativity. Recent research suggests that the number of colours people see, and what they call them, depends on their language.

Explanation

Sunlight enters a raindrop and bends at its surface. Some of it reflects off the back of the drop and bends again as it leaves. Most of this returning light comes out at angles between 0° and 42°, and the brightest light is at about 42°. This angle does not depend on the size of the drop, but it does depend on the refractive index of the water. Sea spray has a different refractive index from rain water, so a "rainbow" in sea spray is a little smaller than a true rainbow. The brightest band is linked to the idea of a caustic (see Caustic (optics)). Light is split into colours because each colour bends by a different amount, a effect called dispersion. Blue light appears on the inside of the rainbow's arc and red on the outside. This splitting also makes the rainbow a little less bright.

A rainbow is not in one fixed place. Each viewer sees their own rainbow, made by the raindrops that send light to their eyes. The rainbow looks curved because these drops lie on a cone with the viewer at its tip, and the whole setup has axial symmetry. Usually at least half of the circle is below the horizon, so most people see only an arc. From an aeroplane, or in a fountain or waterfall spray, a full circle may be seen. When the Sun is high, above 42 degrees, no rainbow is visible in the sky. The angle of the rainbow can be worked out using Snell's law, a rule about how light bends. The rainbow forms at the point where the angle reaches its highest value (an extremum). For red light, the radius angle is about 42.5°, and for blue light it is about 40.6°. These values come from the dispersion relation of water.

Variations

Main article: Monochrome rainbow

Main article: Moonbow

Main article: Fog bow

Main article: Extraterrestrial skies

A rainbow can sometimes have a second, fainter rainbow above it. When both are visible, this is called a double rainbow. The second rainbow is made by two reflections of sunlight inside the water droplets, so its colours appear in reverse order. The dark band between the two is called Alexander's band, after Alexander of Aphrodisias, who first described it. Other kinds include the very rare twinned rainbow, which splits from a single base, and the full-circle rainbow, which can be seen from a high place such as a building or an aircraft. Faint, pastel-coloured bands called supernumerary bands can sometimes appear along the inside edge of a rainbow. They are caused by very small droplets.

Some rainbows form under special conditions. A monochrome or red rainbow may appear at sunrise or sunset, when most blue and green light has been removed. Rainbows can also form from moonlight. These are called moonbows and are much dimmer. Fog bows form from very small droplets and are almost white, while sleetbows form when light passes through falling sleet. Rainbows with more internal reflections are very hard to see. The third-order rainbow was first photographed in 2011. Some arcs look like rainbows but are not, such as the circumzenithal and circumhorizontal arcs, which form from ice crystals. It has been suggested that rainbows might also exist on Saturn's moon Titan, where the liquid is methane instead of water.

Scientific history

The ancient Greek scholar Aristotle was the first to study the rainbow seriously, and his explanation stayed influential for centuries. The Roman philosopher Seneca the Younger discussed many ideas about rainbows in his Naturales Quaestiones (c. 65 AD). He noticed that rainbows always appear opposite the Sun and can be seen in water sprayed by a rower, in water spat by a fuller onto clothes, or in water sprayed through a small hole in a burst pipe. The Arab physicist and polymath Ibn al-Haytham tried to explain the rainbow scientifically, but his idea could not be tested by experimental checks. This idea was repeated by Averroes and helped lead to later correct explanations. In Song dynasty China (960–1279), a polymath scholar-official named Shen Kuo suggested that rainbows form when sunlight meets raindrops in the air. Paul Dong writes that his explanation of the rainbow as a result of atmospheric refraction "is basically in accord with modern scientific principles."

The Persian astronomer Qutb al-Din al-Shirazi gave a fairly accurate explanation of the rainbow, and his student Kamāl al-Dīn al-Fārisī gave a more mathematically satisfying one. Al-Fārisī used a water-filled glass sphere inside a camera obscura-like setup with a controlled aperture to show that the colours of the rainbow come from light being separated. In Europe, Ibn al-Haytham's Book of Optics was translated into Latin and studied by Robert Grosseteste, and his work was continued by Roger Bacon, who wrote about the rainbow in his Opus Majus of 1268. Bacon was the first to calculate the angular size of the rainbow. Theodoric of Freiberg gave an accurate explanation of both the primary and secondary rainbows in 1307.

Later, Descartes advanced this explanation in his 1637 work, Discourse on Method (Discours de la Méthode), and correctly calculated the angles for both bows. Isaac Newton showed that white light is made of all the colours of the rainbow, which a prism can separate, and his work gave the first scientific explanation of the rainbow's main features. A full explanation of the extra bands called supernumerary rainbows came when Thomas Young realised that light can act as a wave and interfere with itself. Later, George Biddell Airy explained how the strength of the colours depends on the size of the water droplets. Modern descriptions of the rainbow are based on Mie scattering, work published by Gustav Mie in 1908, and Nussenzveig provides a modern overview.

Experiments

Experiments with artificial raindrops, which are water-filled spherical flasks, go back at least to Theodoric of Freiberg in the 14th century. Later, Descartes also studied the rainbow using a Florence flask. A flask experiment called Florence's rainbow is still often used today to show how rainbows form. A water-filled flask is lit with parallel white light through a hole in a screen, and a rainbow appears on the screen if the screen is large enough. Because the artificial raindrop is different from a real one, its rainbows look slightly different from natural rainbows.

A similar experiment uses a glass cylinder filled with water, or a solid transparent cylinder, lit either parallel to its round base or at an angle. When the light comes in at an angle, the rainbow angles change compared with the natural rainbow. Other experiments use small liquid drops.

Religion, culture and mythology

See also: Rainbow flag

Rainbows appear often in mythology and have been used in the arts. In the Epic of Gilgamesh, a rainbow appears after a flood, and a similar rainbow appears in the Book of Genesis as part of the flood story of Noah. In Norse mythology, the rainbow bridge Bifröst connects the world of men (Midgard) with the realm of the gods (Asgard). Cuchavira was the rainbow god of the Muisca in present-day Colombia. When the regular rains on the Bogotá savanna ended, the people thanked him with gold, snails and small emeralds. Some forms of Tibetan Buddhism or Dzogchen refer to a rainbow body. In Irish stories, a leprechaun's secret hiding place for his pot of gold is usually said to be at the end of the rainbow. In Greek mythology, the goddess Iris represents the rainbow. She is a messenger goddess who, like the rainbow, connects the mortal world with the gods. In Albanian folk beliefs, the rainbow is seen as the belt of the goddess Prende, and oral legend says that anyone who jumps over the rainbow changes their sex.

In heraldry, the rainbow is shown with 4 bands of colour (argent, gules, or, and vert), with its ends resting on clouds. Examples appear in the coats of arms of the towns of Regen and Pfreimd, both in Bavaria, Germany, and Bouffémont, France, and of the 69th Infantry Regiment (New York) of the United States Army National Guard. Rainbow flags have been used for centuries. They were a symbol of the Cooperative movement in the German Peasants' War in the 16th century, and of peace in Italy. Today the rainbow is a symbol of LGBT social movements, and the rainbow flag as a symbol of LGBT pride is used during June pride month. Gilbert Baker designed it in 1978. In 1994, Archbishop Desmond Tutu and President Nelson Mandela described newly democratic, post-apartheid South Africa as the rainbow nation. The rainbow has also been used in technology product logos, including the Apple Computer logo. Many political alliances across several parties have called themselves a "Rainbow Coalition". Pointing at rainbows has been considered taboo in many cultures.