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This effect is called dispersion. Blue light shorter wavelength is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside.

The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. A "rainbow" formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow. The light at the back of the raindrop does not undergo total internal reflection , and some light does emerge from the back.

However, light coming out the back of the raindrop does not create a rainbow between the observer and the sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow. A rainbow does not exist at one particular location.

Many rainbows exist; however, only one can be seen depending on the particular observer's viewpoint as droplets of light illuminated by the sun.

All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. This light is what constitutes the rainbow for that observer.

The whole system composed by the sun's rays, the observer's head, and the spherical water drops has an axial symmetry around the axis through the observer's head and parallel to the sun's rays. The rainbow is curved because the set of all the raindrops that have the right angle between the observer, the drop, and the sun, lie on a cone pointing at the sun with the observer at the tip. We can determine the perceived angle which the rainbow subtends as follows.

The term double rainbow is used when both the primary and secondary rainbows are visible. In theory, all rainbows are double rainbows, but since the secondary bow is always fainter than the primary, it may be too weak to spot in practice.

Secondary rainbows are caused by a double reflection of sunlight inside the water droplets. As a result of the "inside" of the secondary bow being "up" to the observer, the colours appear reversed compared to those of the primary bow.

The secondary rainbow is fainter than the primary because more light escapes from two reflections compared to one and because the rainbow itself is spread over a greater area of the sky. Each rainbow reflects white light inside its coloured bands, but that is "down" for the primary and "up" for the secondary.

Unlike a double rainbow that consists of two separate and concentric rainbow arcs, the very rare twinned rainbow appears as two rainbow arcs that split from a single base.

A "normal" secondary rainbow may be present as well. Twinned rainbows can look similar to, but should not be confused with supernumerary bands. The two phenomena may be told apart by their difference in colour profile: The cause of a twinned rainbow is the combination of different sizes of water drops falling from the sky. Due to air resistance, raindrops flatten as they fall, and flattening is more prominent in larger water drops.

When two rain showers with different-sized raindrops combine, they each produce slightly different rainbows which may combine and form a twinned rainbow. That small difference in droplet size resulted in a small difference in flattening of the droplet shape, and a large difference in flattening of the rainbow top.

Meanwhile, the even rarer case of a rainbow split into three branches was observed and photographed in nature. In theory, every rainbow is a circle, but from the ground, only its upper half can be seen.

Viewing the rainbow's lower half requires the presence of water droplets below the observer's horizon, as well as sunlight that is able to reach them. These requirements are not usually met when the viewer is at ground level, either because droplets are absent in the required position, or because the sunlight is obstructed by the landscape behind the observer. From a high viewpoint such as a high building or an aircraft, however, the requirements can be met and the full-circle rainbow can be seen.

A circular rainbow should not be confused with the glory , which is much smaller in diameter and is created by different optical processes. In the right circumstances, a glory and a circular rainbow or fog bow can occur together. In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i. These extra bands are called supernumerary rainbows or supernumerary bands ; together with the rainbow itself the phenomenon is also known as a stacker rainbow.

The supernumerary bows are slightly detached from the main bow, become successively fainter along with their distance from it, and have pastel colours consisting mainly of pink, purple and green hues rather than the usual spectrum pattern.

Supernumerary rainbows cannot be explained using classical geometric optics. The alternating faint bands are caused by interference between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in phase , reinforcing each other through constructive interference , creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interference , and creating a gap. Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow.

Supernumerary rainbows are clearest when raindrops are small and of uniform size. The very existence of supernumerary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in When a rainbow appears above a body of water, two complementary mirror bows may be seen below and above the horizon, originating from different light paths. Their names are slightly different.

A reflected rainbow may appear in the water surface below the horizon. The reflected rainbow is frequently visible, at least partially, even in small puddles. A reflection rainbow may be produced where sunlight reflects off a body of water before reaching the raindrops see diagram and [1] , if the water body is large, quiet over its entire surface, and close to the rain curtain.

The reflection rainbow appears above the horizon. It intersects the normal rainbow at the horizon, and its arc reaches higher in the sky, with its centre as high above the horizon as the normal rainbow's centre is below it. Due to the combination of requirements, a reflection rainbow is rarely visible. Up to eight separate bows may be distinguished if the reflected and reflection rainbows happen to occur simultaneously: The normal non-reflection primary and secondary bows above the horizon 1, 2 with their reflected counterparts below it 3, 4 , and the reflection primary and secondary bows above the horizon 5, 6 with their reflected counterparts below it 7, 8.

Occasionally a shower may happen at sunrise or sunset, where the shorter wavelengths like blue and green have been scattered and essentially removed from the spectrum. Further scattering may occur due to the rain, and the result can be the rare and dramatic monochrome or red rainbow.

In addition to the common primary and secondary rainbows, it is also possible for rainbows of higher orders to form. The order of a rainbow is determined by the number of light reflections inside the water droplets that create it: One reflection results in the first-order or primary rainbow; two reflections create the second-order or secondary rainbow.

More internal reflections cause bows of higher orders—theoretically unto infinity. For these reasons, naturally occurring rainbows of an order higher than 2 are rarely visible to the naked eye. Nevertheless, sightings of the third-order bow in nature have been reported, and in it was photographed definitively for the first time. In a laboratory setting, it is possible to create bows of much higher orders.

Felix Billet — depicted angular positions up to the 19th-order rainbow, a pattern he called a "rose of rainbows". Up to the th-order rainbow was reported by Ng et al. Tertiary and quaternary rainbows should not be confused with "triple" and "quadruple" rainbows—terms sometimes erroneously used to refer to the—much more common—supernumerary bows and reflection rainbows.

Like most atmospheric optical phenomena, rainbows can be caused by light from the Sun, but also from the Moon. In case of the latter, the rainbow is referred to as a lunar rainbow or moonbow. They are much dimmer and rarer than solar rainbows, requiring the Moon to be near-full in order for them to be seen.

For the same reason, moonbows are often perceived as white and may be thought of as monochrome. The full spectrum is present, however, but the human eye is not normally sensitive enough to see the colours. Long exposure photographs will sometimes show the colour in this type of rainbow. Fogbows form in the same way as rainbows, but they are formed by much smaller cloud and fog droplets that diffract light extensively. They are almost white with faint reds on the outside and blues inside; often one or more broad supernumerary bands can be discerned inside the inner edge.

The colours are dim because the bow in each colour is very broad and the colours overlap. Fogbows are commonly seen over water when air in contact with the cooler water is chilled, but they can be found anywhere if the fog is thin enough for the sun to shine through and the sun is fairly bright.

They are very large—almost as big as a rainbow and much broader. They sometimes appear with a glory at the bow's centre.

Fog bows should not be confused with ice halos , which are very common around the world and visible much more often than rainbows of any order , [57] yet are unrelated to rainbows.

The circumzenithal and circumhorizontal arcs are two related optical phenomena similar in appearance to a rainbow, but unlike the latter, their origin lies in light refraction through hexagonal ice crystals rather than liquid water droplets. This means that they are not rainbows, but members of the large family of halos. Both arcs are brightly coloured ring segments centred on the zenith , but in different positions in the sky: The circumzenithal arc is notably curved and located high above the Sun or Moon with its convex side pointing downwards creating the impression of an "upside down rainbow" ; the circumhorizontal arc runs much closer to the horizon, is more straight and located at a significant distance below the Sun or Moon.

Both arcs have their red side pointing towards the sun and their violet part away from it, meaning the circumzenithal arc is red on the bottom, while the circumhorizontal arc is red on top. The circumhorizontal arc is sometimes referred to by the misnomer "fire rainbow". It has been suggested that rainbows might exist on Saturn 's moon Titan , as it has a wet surface and humid clouds.

Although visible rainbows may be rare due to Titan's hazy skies , infrared rainbows may be more common, but an observer would need infrared night vision goggles to see them. Droplets or spheres composed of materials with different refractive indices than plain water produce rainbows with different radius angles.

Since salt water has a higher refractive index, a sea spray bow doesn't perfectly align with the ordinary rainbow, if seen at the same spot. Due to a much higher refractive index, rainbows observed on such marbles have a noticeably smaller radius. The displacement of the rainbow due to different refractive indices can be pushed to a peculiar limit. For a material with a refractive index larger than 2, there is no angle fulfilling the requirements for the first order rainbow.

For example, the index of refraction of diamond is about 2. This results in a rainbow of the n -th order shrinking to the antisolar point and vanishing. The classical Greek scholar Aristotle — BC was first to devote serious attention to the rainbow. Lee and Alistair B. Fraser, "Despite its many flaws and its appeal to Pythagorean numerology, Aristotle's qualitative explanation showed an inventiveness and relative consistency that was unmatched for centuries.

After Aristotle's death, much rainbow theory consisted of reaction to his work, although not all of this was uncritical. In Book I of Naturales Quaestiones c. He notices that rainbows appear always opposite to the sun, that they appear in water sprayed by a rower, in the water spat by a fuller on clothes stretched on pegs or by water sprayed through a small hole in a burst pipe.

He even speaks of rainbows produced by small rods virgulae of glass, anticipating Newton's experiences with prisms. He takes into account two theories: He also discusses other phenomena related to rainbows: In his Maqala fi al-Hala wa Qaws Quzah On the Rainbow and Halo , al-Haytham "explained the formation of rainbow as an image, which forms at a concave mirror. If the rays of light coming from a farther light source reflect to any point on axis of the concave mirror, they form concentric circles in that point.

When it is supposed that the sun as a farther light source, the eye of viewer as a point on the axis of mirror and a cloud as a reflecting surface, then it can be observed the concentric circles are forming on the axis. The cloud, he thought, serves simply as the background of this thin substance, much as a quicksilver lining is placed upon the rear surface of the glass in a mirror. In Song Dynasty China — , a polymath scholar-official named Shen Kuo — hypothesised—as a certain Sun Sikong — did before him—that rainbows were formed by a phenomenon of sunlight encountering droplets of rain in the air.

According to Nader El-Bizri, the Persian astronomer , Qutb al-Din al-Shirazi — , gave a fairly accurate explanation for the rainbow phenomenon. He "proposed a model where the ray of light from the sun was refracted twice by a water droplet, one or more reflections occurring between the two refractions. He then placed this model within a camera obscura that has a controlled aperture for the introduction of light. He projected light unto the sphere and ultimately deduced through several trials and detailed observations of reflections and refractions of light that the colours of the rainbow are phenomena of the decomposition of light.

His work on light was continued by Roger Bacon , who wrote in his Opus Majus of about experiments with light shining through crystals and water droplets showing the colours of the rainbow. He explained the primary rainbow, noting that "when sunlight falls on individual drops of moisture, the rays undergo two refractions upon ingress and egress and one reflection at the back of the drop before transmission into the eye of the observer. Descartes ' treatise, Discourse on Method , further advanced this explanation.

Knowing that the size of raindrops did not appear to affect the observed rainbow, he experimented with passing rays of light through a large glass sphere filled with water. By measuring the angles that the rays emerged, he concluded that the primary bow was caused by a single internal reflection inside the raindrop and that a secondary bow could be caused by two internal reflections.

He supported this conclusion with a derivation of the law of refraction subsequently to, but independently of, Snell and correctly calculated the angles for both bows. His explanation of the colours, however, was based on a mechanical version of the traditional theory that colours were produced by a modification of white light.

Isaac Newton demonstrated that white light was composed of the light of all the colours of the rainbow, which a glass prism could separate into the full spectrum of colours, rejecting the theory that the colours were produced by a modification of white light. He also showed that red light is refracted less than blue light, which led to the first scientific explanation of the major features of the rainbow. Young's work was refined in the s by George Biddell Airy , who explained the dependence of the strength of the colours of the rainbow on the size of the water droplets.

For example, Nussenzveig provides a modern overview. Experiments on the rainbow phenomenon using artificial raindrops, i. Later, also Descartes studied the phenomenon using a Florence flask.

A flask experiment known as Florence's rainbow is still often used today as an imposing and intuitively accessible demonstration experiment of the rainbow phenomenon.

Due to the finite wall thickness and the macroscopic character of the artificial raindrop, several subtle differences exist as compared to the natural phenomenon, [86] [87] including slightly changed rainbow angles and a splitting of the rainbow orders.

A very similar experiment consists in using a cylindrical glass vessel filled with water or a solid transparent cylinder and illuminated either parallel to the circular base i. Under these latter conditions the rainbow angles change relative to the natural phenomenon since the effective index of refraction of water changes Bravais' index of refraction for inclined rays applies.

Other experiments use small liquid drops, [52] [53] see text above. Rainbows occur frequently in mythology , and have been used in the arts.

One of the earliest literary occurrences of a rainbow is in the Book of Genesis chapter 9, as part of the flood story of Noah, where it is a sign of God's covenant to never destroy all life on earth with a global flood again. The Irish leprechaun 's secret hiding place for his pot of gold is usually said to be at the end of the rainbow. This place is appropriately impossible to reach, because the rainbow is an optical effect which cannot be approached.

Rainbows sometimes appear in heraldry too, even if its characteristic of multiple colours doesn't really fit into the usual heraldic style. Rainbow flags have been used for centuries.

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