Rainbow

A rainbow is an optical phenomenon that appears in the sky. It forms when refraction, internal reflection and dispersion of light happen in water droplets. These processes spread light out into a band of colours called a spectrum. The colours form a curved arc. Rainbows made 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. They can also come from mist, spray, and tiny drops of dew in the air.

When seen from the ground, a rainbow usually looks like a glowing arc. When you are flying, a rainbow can look like a full circle if there is enough mist. The middle of the curve is always in line with the Sun and your eyes.

In a main 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 are in reverse order, with red on the lower side of the arc.

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

Visibility

You can see rainbows when 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 the sky is clear in the direction of the Sun. A larger but fainter secondary rainbow is often visible too. Rainbows are also common near waterfalls or fountains. Sometimes, 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. It would need an angle of view of 84°. With a 35 mm camera, you would need a wide-angle lens with a focal length of 19 mm or less. 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 split the spectrum into five main colours in 1672: red, yellow, green, blue and violet. Later, he added orange and indigo, making seven colours. This matched the seven notes in a musical scale. His choice was partly based on ideas from ancient Greek sophists. They 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. 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. Light is split into colours because each colour bends by a different amount. This is 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

Sometimes a rainbow has a second, fainter rainbow above it. This is called a double rainbow. The colours of the second rainbow are in the opposite order. A dark band between the two is called Alexander's band, after Alexander of Aphrodisias, who first described it. Other kinds of rainbows are also possible. A twinned rainbow is very rare and starts from a single base. A full-circle rainbow 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 form from very tiny droplets.

Some rainbows form in special conditions. A monochrome or red rainbow may appear at sunrise or sunset. Rainbows can also form from moonlight. These are called moonbows, and they are much dimmer. Fog bows are made from very small droplets and look almost white. Sleetbows form when light passes through falling sleet. Rainbows with more reflections inside the droplets 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. They form from ice crystals. Scientists have 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. His ideas were trusted for many centuries. The Roman philosopher Seneca the Younger wrote about rainbows in his Naturales Quaestiones (c. 65 AD). He noticed that rainbows always appear opposite the Sun. He also saw them in water sprayed by a rower, in water spat by a fuller onto clothes, and in water sprayed through a small hole in a broken pipe. The Arab physicist and polymath Ibn al-Haytham tried to explain the rainbow scientifically. His idea could not be tested by experimental checks. Averroes repeated this idea, and it 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. His student Kamāl al-Dīn al-Fārisī gave a clearer explanation using mathematics. Al-Fārisī used a glass ball filled with water. He placed it in a camera obscura-like setup with a controlled aperture. This showed 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. 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. In 1307, Theodoric of Freiberg gave an accurate explanation of both the primary and secondary rainbows.

Later, Descartes improved this explanation in his 1637 work, Discourse on Method (Discours de la Méthode). He correctly calculated the angles for both bows. Isaac Newton showed that white light is made of all the colours of the rainbow. A prism can separate these colours. His work gave the first scientific explanation of the rainbow's main features. Later, Thomas Young explained the extra bands called supernumerary rainbows. He realised that light can act as a wave and interfere with itself. George Biddell Airy then 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. Gustav Mie published this work in 1908, and Nussenzveig provides a modern overview.

Experiments

People have tried making artificial raindrops, which are water-filled glass balls, since at least Theodoric of Freiberg in the 14th century. Later, Descartes also studied rainbows using a Florence flask. Today, a flask experiment called Florence's rainbow is still often used to show how rainbows form. A water-filled flask is lit with white light through a small hole in a screen. If the screen is large enough, a rainbow appears on it. Because the artificial raindrop is not exactly like a real one, its rainbows look a little different from natural ones.

A similar experiment uses a glass cylinder filled with water, or a solid clear cylinder. The light can shine on its round base or at an angle. When the light comes in at an angle, the rainbow looks different from a natural one. Other experiments use small drops of liquid.

Religion, culture and mythology

See also: Rainbow flag

Rainbows appear often in myths and have been used in art. In the Epic of Gilgamesh, a rainbow appears after a flood. A similar rainbow appears in the Book of Genesis, in the flood story of Noah. In Norse mythology, the rainbow bridge Bifröst connects the world of people (Midgard) with the home of the gods (Asgard). Cuchavira was the rainbow god of the Muisca people, who lived in what is now Colombia. When the regular rains on the Bogotá savanna stopped, the people thanked him with gold, snails and small emeralds. Some forms of Tibetan Buddhism or Dzogchen talk about a rainbow body. In Irish stories, a leprechaun hides his pot of gold at the end of the rainbow. In Greek mythology, the goddess Iris is the rainbow. She is a messenger who, like the rainbow, connects the human world with the gods. In Albanian folk beliefs, the rainbow is seen as the belt of the goddess Prende.

In heraldry, the rainbow is shown with 4 bands of colour (argent, gules, or, and vert), with its ends resting on clouds. It appears in the coats of arms of the towns of Regen and Pfreimd, both in Bavaria, Germany, and Bouffémont, France. It also appears in the coat of arms 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. 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 the new, democratic South Africa after apartheid as the rainbow nation. The rainbow has also been used in technology logos, including the Apple Computer logo. Many political groups from different parties have called themselves a "Rainbow Coalition". In many cultures, pointing at rainbows has been seen as rude.