A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.
Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground, and centered on a line from the sun to the observer's eye.
In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.
In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, with red on the inner side of the arc. This is caused by the light being reflected twice on the inside of the droplet before leaving it.
A rainbow is not located at a specific distance from the observer, but comes from an optical illusion caused by any water droplets viewed from a certain angle relative to a light source. Thus, a rainbow is not an object and cannot be physically approached. Indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems "under" or "at the end of" a rainbow, the second observer will see a different rainbow—farther off—at the same angle as seen by the first observer.
Rainbows span a continuous spectrum of colours. Any distinct bands perceived are an artefact of human colour vision, and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side. For colours seen by the human eye, the most commonly cited and remembered sequence is Newton's sevenfold red, orange, yellow, green, blue, indigo and violet, remembered by the mnemonic Richard Of York Gave Battle In Vain (ROYGBIV).
Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.
Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle. Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening. The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the sun. The result is a luminous rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible. It appears about 10° outside of the primary rainbow, with inverse order of colours.
The rainbow effect is also commonly seen near waterfalls or fountains. In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white.
It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an angle of view of 84°. For a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be required. Now that software for stitching several images into a panorama is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames.
From above the earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle. This phenomenon can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°.
The sky inside a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light over an entire circular disc in the sky. The radius of the disc depends on the wavelength of light, with red light being scattered over a larger angle than blue light. Over most of the disc, scattered light at all wavelengths overlaps, resulting in white light which brightens the sky. At the edge, the wavelength dependence of the scattering gives rise to the rainbow.
A spectrum obtained using a glass prism and a point source is a continuum of wavelengths without bands. The number of colours that the human eye is able to distinguish in a spectrum is in the order of 100. Accordingly, the Munsell colour system (a 20th-century system for numerically describing colours, based on equal steps for human visual perception) distinguishes 100 hues. The apparent discreteness of main colours is an artefact of human perception and the exact number of main colours is a somewhat arbitrary choice.
Newton, who admitted his eyes were not very critical in distinguishing colours, originally (1672) divided the spectrum into five main colours: red, yellow, green, blue and violet. Later he included orange and indigo, giving seven main colours by analogy to the number of notes in a musical scale. Newton chose to divide the visible spectrum into seven colours out of a belief derived from the beliefs of the ancient Greek sophists, who thought there was a connection between the colours, the musical notes, the known objects in the Solar System, and the days of the week. Scholars have noted that what Newton regarded at the time as "blue" would today be regarded as cyan, and what Newton called "indigo" would today be considered blue.
According to Isaac Asimov, "It is customary to list indigo as a colour lying between blue and violet, but it has never seemed to me that indigo is worth the dignity of being considered a separate colour. To my eyes it seems merely deep blue."
The colour pattern of a rainbow is different from a spectrum, and the colours are less saturated. There is spectral smearing in a rainbow owing to the fact that for any particular wavelength, there is a distribution of exit angles, rather than a single unvarying angle. In addition, a rainbow is a blurred version of the bow obtained from a point source, because the disk diameter of the sun (0.5°) cannot be neglected compared to the width of a rainbow (2°). The number of colour bands of a rainbow may therefore be different from the number of bands in a spectrum, especially if the droplets are particularly large or small. Therefore, the number of colours of a rainbow is variable. If, however, the word rainbow is used inaccurately to mean spectrum, it is the number of main colours in the spectrum.
The question of whether everyone sees seven colours in a rainbow is related to the idea of linguistic relativity. Suggestions have been made that there is universality in the way that a rainbow is perceived. However, more recent research suggests that the number of distinct colours observed and what these are called depend on the language that one uses with people whose language has fewer colour words seeing fewer discrete colour bands.
When sunlight encounters a raindrop, part of the light is reflected and the rest enters the raindrop. The light is refracted at the surface of the raindrop. When this light hits the back of the raindrop, some of it is reflected off the back. When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop. (The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow.) The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°. This angle is independent of the size of the drop, but does depend on its refractive index. Seawater has a higher refractive index than rain water, so the radius of a "rainbow" in sea spray is smaller than a true rainbow. This is visible to the naked eye by a misalignment of these bows.
The reason the returning light is most intense at about 42° is that this is a turning point – light hitting the outermost ring of the drop gets returned at less than 42°, as does the light hitting the drop nearer to its centre. There is a circular band of light that all gets returned right around 42°. If the sun were a laser emitting parallel, monochromatic rays, then the luminance (brightness) of the bow would tend toward infinity at this angle (ignoring interference effects). (See Caustic (optics).) But since the sun's luminance is finite and its rays are not all parallel (it covers about half a degree of the sky) the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its wavelength, and hence its colour. 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. The base of the cone forms a circle at an angle of 40–42° to the line between the observer's head and their shadow but 50% or more of the circle is below the horizon, unless the observer is sufficiently far above the earth's surface to see it all, for example in an aeroplane (see above). Alternatively, an observer with the right vantage point may see the full circle in a fountain or waterfall spray.
We can determine the perceived angle which the rainbow subtends as follows.
Given a spherical raindrop, and defining the perceived angle of the rainbow as 2φ, and the angle of the internal reflection as 2β, then the angle of incidence of the sun's rays with respect to the drop's surface normal is 2β − φ. Since the angle of refraction is β, Snell's law gives us
where n = 1.333 is the refractive index of water. Solving for φ, we get
The rainbow will occur where the angle φ is maximum with respect to the angle β. Therefore, from calculus, we can set dφ/dβ = 0, and solve for β, which yields
Substituting back into the earlier equation for φ yields 2φmax ≈ 42° as the radius angle of the rainbow.
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. Technically the secondary bow is centred on the sun itself, but since its angular size is more than 90° (about 127° for violet to 130° for red), it is seen on the same side of the sky as the primary rainbow, about 10° outside it at an apparent angle of 50–53°. 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. The dark area of unlit sky lying between the primary and secondary bows is called Alexander's band, after Alexander of Aphrodisias who first described it.
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. The colours in the second bow, rather than reversing as in a secondary rainbow, appear in the same order as the primary rainbow. 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: supernumerary bands consist of subdued pastel hues (mainly pink, purple and green), while the twinned rainbow shows the same spectrum as a regular rainbow. 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. A numerical ray tracing study showed that a twinned rainbow on a photo could be explained by a mixture of 0.40 and 0.45 mm droplets. 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, usually only its upper half can be seen. Since the rainbow's centre is diametrically opposed to the sun's position in the sky, more of the circle comes into view as the sun approaches the horizon, meaning that the largest section of the circle normally seen is about 50% during sunset or sunrise. 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. Like a partial rainbow, the circular rainbow can have a secondary bow or supernumerary bows as well. It is possible to produce the full circle when standing on the ground, for example by spraying a water mist from a garden hose while facing away from the sun.
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. Another atmospheric phenomenon that may be mistaken for a "circular rainbow" is the 22° halo, which is caused by ice crystals rather than liquid water droplets, and is located around the sun (or moon), not opposite it.
In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i.e., inside the primary bow or, much more rarely, outside the secondary. 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. The effect becomes apparent when water droplets are involved that have a diameter of about 1 mm or less; the smaller the droplets are, the broader the supernumerary bands become, and the less saturated their colours. Due to their origin in small droplets, supernumerary bands tend to be particularly prominent in fogbows.
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 1804.
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 sunlight is first deflected by the raindrops, and then reflected off the body of water, before reaching the observer. 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 ), 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. As more and more light is lost with each internal reflection, however, each subsequent bow becomes progressively dimmer and therefore increasingly harder to spot. An additional challenge in observing the third-order (or tertiary) and fourth-order (quaternary) rainbows is their location in the direction of the sun (about 40° and 45° from the sun, respectively), causing them to become drowned in its glare.
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 2011 it was photographed definitively for the first time. Shortly after, the fourth-order rainbow was photographed as well, and in 2014 the first ever pictures of the fifth-order (or quinary) rainbow, located in between the primary and secondary bows, were published.
In a laboratory setting, it is possible to create bows of much higher orders. Felix Billet (1808–1882) depicted angular positions up to the 19th-order rainbow, a pattern he called a "rose of rainbows". In the laboratory, it is possible to observe higher-order rainbows by using extremely bright and well collimated light produced by lasers. Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam.
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.
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". In order to view it, the Sun or Moon must be at least 58° above the horizon, making it a rare occurrence at higher latitudes. The circumzenithal arc, visible only at a solar or lunar elevation of less than 32°, is much more common, but often missed since it occurs almost directly overhead.
It has been suggested that rainbows might exist on Saturn's moon Titan, as it has a wet surface and humid clouds. The radius of a Titan rainbow would be about 49° instead of 42°, because the fluid in that cold environment is methane instead of water. 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. Tiny plastic or glass marbles may be used in road marking as a reflectors to enhance its visibility by drivers at night. Due to a much higher refractive index, rainbows observed on such marbles have a noticeably smaller radius. One can easily reproduce such phenomena by sprinkling liquids of different refractive indices in the air, as illustrated in the photo.
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 2.4, so diamond spheres would produce rainbows starting from the second order, omitting the first order. In general, as the refractive index exceeds a number n+1, where n is a natural number, the critical incidence angle for n times internally reflected rays escapes the domain . This results in a rainbow of the n-th order shrinking to the antisolar point and vanishing.
The classical Greek scholar Aristotle (384–322 BC) was first to devote serious attention to the rainbow. According to Raymond L. 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. 65 AD), the Roman philosopher Seneca the Younger discusses various theories of the formation of rainbows extensively, including those of Aristotle. 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: one, that the rainbow is produced by the sun reflecting in each water drop, the other, that it is produced by the sun reflected in a cloud shaped like a concave mirror; he favours the latter. He also discusses other phenomena related to rainbows: the mysterious "virgae" (rods), halos and parhelia.
According to Hüseyin Gazi Topdemir, the Arab physicist and polymath Ibn al-Haytham (Alhazen; 965–1039), attempted to provide a scientific explanation for the rainbow phenomenon. 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." He was not able to verify this because his theory that "light from the sun is reflected by a cloud before reaching the eye" did not allow for a possible experimental verification. This explanation was later repeated by Averroes, and, though incorrect, provided the groundwork for the correct explanations later given by Kamāl al-Dīn al-Fārisī (1267–1319) and Theodoric of Freiberg (c.1250–1310).
Ibn al-Haytham's contemporary, the Persian philosopher and polymath Ibn Sīnā (Avicenna; 980–1037), provided an alternative explanation, writing "that the bow is not formed in the dark cloud but rather in the very thin mist lying between the cloud and the sun or observer. 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. Ibn Sīnā would change the place not only of the bow, but also of the colour formation, holding the iridescence to be merely a subjective sensation in the eye." This explanation, however, was also incorrect. Ibn Sīnā's account accepts many of Aristotle's arguments on the rainbow.
In Song Dynasty China (960–1279), a polymath scholar-official named Shen Kuo (1031–1095) hypothesised—as a certain Sun Sikong (1015–1076) did before him—that rainbows were formed by a phenomenon of sunlight encountering droplets of rain in the air. Paul Dong writes that Shen's explanation of the rainbow as a phenomenon of atmospheric refraction "is basically in accord with modern scientific principles."
According to Nader El-Bizri, the Persian astronomer, Qutb al-Din al-Shirazi (1236–1311), gave a fairly accurate explanation for the rainbow phenomenon. This was elaborated on by his student, Kamāl al-Dīn al-Fārisī (1267–1319), who gave a more mathematically satisfactory explanation of the rainbow. 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." An experiment with a water-filled glass sphere was conducted and al-Farisi showed the additional refractions due to the glass could be ignored in his model. As he noted in his Kitab Tanqih al-Manazir (The Revision of the Optics), al-Farisi used a large clear vessel of glass in the shape of a sphere, which was filled with water, in order to have an experimental large-scale model of a rain drop. 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.
In Europe, Ibn al-Haytham's Book of Optics was translated into Latin and studied by Robert Grosseteste. His work on light was continued by Roger Bacon, who wrote in his Opus Majus of 1268 about experiments with light shining through crystals and water droplets showing the colours of the rainbow. In addition, Bacon was the first to calculate the angular size of the rainbow. He stated that the rainbow summit can not appear higher than 42° above the horizon. Theodoric of Freiberg is known to have given an accurate theoretical explanation of both the primary and secondary rainbows in 1307. 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." He explained the secondary rainbow through a similar analysis involving two refractions and two reflections.
Descartes' 1637 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. Newton's corpuscular theory of light was unable to explain supernumerary rainbows, and a satisfactory explanation was not found until Thomas Young realised that light behaves as a wave under certain conditions, and can interfere with itself.
Young's work was refined in the 1820s by George Biddell Airy, who explained the dependence of the strength of the colours of the rainbow on the size of the water droplets. Modern physical descriptions of the rainbow are based on Mie scattering, work published by Gustav Mie in 1908. Advances in computational methods and optical theory continue to lead to a fuller understanding of rainbows. For example, Nussenzveig provides a modern overview.
Experiments on the rainbow phenomenon using artificial raindrops, i.e. water-filled spherical flasks, go back at least to Theodoric of Freiberg in the 14th century. 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. It consists in illuminating (with parallel white light) a water-filled spherical flask through a hole in a screen. A rainbow will then appear thrown back / projected on the screen, provided the screen is large enough. Due to the finite wall thickness and the macroscopic character of the artificial raindrop, several subtle differences exist as compared to the natural phenomenon, 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.e. light rays remaining at a fixed height while they transit the cylinder) or under an angle to the base. 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).
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. In Norse mythology, the rainbow bridge Bifröst connects the world of men (Midgard) and the realm of the gods (Asgard). Cuchavira was the god of the rainbow for the Muisca in present-day Colombia and when the regular rains on the Bogotá savanna were over, the people thanked him offering gold, snails and small emeralds. 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. It was a symbol of the Cooperative movement in the German Peasants' War in the 16th century, of peace in Italy, and of gay pride and LGBT social movements since the 1970s. 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 spanning multiple political parties have called themselves a "Rainbow Coalition".
approximation obtained by his model was good enough to allow him to ignore the effects of the glass container
AMC Networks Inc. is an American entertainment company headquartered in 11 Penn Plaza, New York, that owns and operates the cable channels AMC (its eponymous brand), IFC, We TV, BBC America (through a joint venture with BBC Studios), and SundanceTV; the art house movie theater IFC Center in New York City; the independent film company IFC Films; and premium streaming services Sundance Now and Shudder. In addition, the company operates AMC Networks International, its global division.
The company was originally launched in 1980 and formerly known as Rainbow Media Holdings, LLC, a subsidiary of Cablevision, but was spun off as a publicly traded company in July 2011. The company is majority-owned and controlled by the Dolan family.Gravity's Rainbow
Gravity's Rainbow is a 1973 novel by American writer Thomas Pynchon.
Lengthy, complex, and featuring a large cast of characters, the narrative is set primarily in Europe at the end of World War II, and centers on the design, production and dispatch of V-2 rockets by the German military. In particular, it features the quest undertaken by several characters to uncover the secret of a mysterious device named the "Schwarzgerät" ("black device"), slated to be installed in a rocket with the serial number "00000".
Traversing a wide range of knowledge, Gravity's Rainbow transgresses boundaries between high and low culture, between literary propriety and profanity, and between science and speculative metaphysics. It shared the 1974 U.S. National Book Award for Fiction with A Crown of Feathers and Other Stories by Isaac Bashevis Singer. Although selected by the Pulitzer Prize jury on fiction for the 1974 Pulitzer Prize for Fiction, the Pulitzer Advisory Board was offended by its content, some of which was described as "'unreadable,' 'turgid,' 'overwritten' and in parts 'obscene'". No Pulitzer Prize was awarded for fiction that year. The novel was nominated for the 1973 Nebula Award for Best Novel.Time named Gravity's Rainbow one of its "All-Time 100 Greatest Novels", a list of the best English-language novels from 1923 to 2005 and it is considered by some critics to be one of the greatest American novels ever written.Hawaii Rainbow Warriors football
The Hawaii Rainbow Warriors football team represents the University of Hawaii at Manoa in NCAA Division I FBS college football. On November 27, 2015, Nick Rolovich was hired as the new head football coach at the University of Hawaii replacing Norm Chow. It was part of the Western Athletic Conference until July 2012, when the team joined the Mountain West Conference.
From 2000 until July 1, 2013, the football team was renamed to simply Warriors, until a 2013 decision to standardize all of the school's athletic team names took effect, and the team was once again known as the Rainbow Warriors.The Hawaiʻi Warriors were the third team from a non automatic qualifier conference to play in a BCS bowl game. They played Georgia in the Sugar Bowl on January 1, 2008 in New Orleans.Israel Kamakawiwoʻole
Israel Kaʻanoʻi Kamakawiwoʻole (Hawaiian pronunciation: [kəˌmɐkəˌvivoˈʔole], translation: "The Fearless Eyed Man") (May 20, 1959 – June 26, 1997), also called Braddah Iz or IZ, was a Native Hawaiian singer-songwriter, musician, and Hawaiian sovereignty activist.
His voice became famous outside Hawaii when his album Facing Future was released in 1993. His medley of "Somewhere Over the Rainbow/What a Wonderful World" was released on his albums Ka ʻAnoʻi and Facing Future. It was subsequently featured in several films, television programs, and television commercials.
Along with his ukulele playing and incorporation of other genres, such as jazz and reggae, Kamakawiwoʻole remains influential in Hawaiian music.LeVar Burton
Levardis Robert Martyn Burton Jr. (born February 16, 1957) is an American actor, presenter, director and author. He is best known for his roles as the host of the long-running PBS children's series Reading Rainbow, Lt. Commander Geordi La Forge in Star Trek: The Next Generation and the young Kunta Kinte in the 1977 award-winning ABC television miniseries Roots. He has also directed a number of television episodes for various iterations of Star Trek, among other programs.Mario Kart
Mario Kart is a series of go-kart-style racing video games developed and published by Nintendo as spin-offs from its trademark Super Mario series. The first in the series, Super Mario Kart, was launched in 1992 on the Super Nintendo Entertainment System to critical and commercial success.There have been six Mario Kart games released for home consoles, three portable games, and four Namco co-developed arcade games, for a total of thirteen. The latest game in the main series, Mario Kart 8 Deluxe, was released on Nintendo Switch in April 2017. The series has sold over 100 million copies worldwide to date.My Little Pony
My Little Pony is a toy line and media franchise mainly targeting girls, developed by American toy company Hasbro. The first toys were developed by Bonnie Zacherle, Charles Muenchinger, and Steve D'Aguanno, and were produced in 1981. The ponies feature colorful bodies, manes and a unique symbol on one or both sides of their flanks. Such symbols are referred to in the two most recent incarnations as "cutie marks". My Little Pony has been revamped several times with new and more modern looks to appeal to a new market.
Following the original My Pretty Pony toy that was introduced in 1981, My Little Pony was launched in 1982 and the line became popular during the 1980s. The original toy line ran from 1982 to 1992 in the United States and to 1995 globally, and two animated specials, an animated feature-length film and two animated television series produced during the period up until 1992. The first incarnation's popularity peaked in 1990, but the following year Hasbro decided to discontinue the toy line due to increased competition. One hundred fifty million ponies were sold in the 1980s.The toy line was revived in 1997, but these toys proved unpopular and were discontinued in 1999. The brand saw a more popular revival in 2003 with toys that more closely resembled the original toy line, which sold approximately 100 million pony toys globally by 2010. Hasbro launched the fourth incarnation of the franchise in 2010, which started with the animated series My Little Pony: Friendship Is Magic. The brand grossed over $650 million in retail sales in 2013, and over $1 billion annually in retail sales in 2014 and 2015.Over the Rainbow
"Over the Rainbow" is a ballad composed by Harold Arlen with lyrics by Yip Harburg. It was written for the movie The Wizard of Oz and was sung by actress Judy Garland in her starring role as Dorothy Gale. It won the Academy Award for Best Original Song and became Garland's signature song.
About five minutes into the film, Dorothy sings the song after failing to get Aunt Em, Uncle Henry, and the farm hands to listen to her story of an unpleasant incident involving her dog, Toto, and the town spinster, Miss Gulch (Margaret Hamilton). Aunt Em tells her to "find yourself a place where you won't get into any trouble". This prompts her to walk off by herself, musing to Toto, "Some place where there isn't any trouble. Do you suppose there is such a place, Toto? There must be. It's not a place you can get to by a boat, or a train. It's far, far away. Behind the moon, beyond the rain...", at which point she begins singing.Rainbow (rock band)
Rainbow (also known as Ritchie Blackmore's Rainbow or Blackmore's Rainbow) are a British rock supergroup led by guitarist Ritchie Blackmore, active from 1975 until 1984, 1993 until 1997, and 2015 until present. They were originally established with Ronnie James Dio's American rock band Elf, but after their first album, Blackmore fired the backing members and continued with Dio until 1979. Three British musicians joined in 1979—singer Graham Bonnet, keyboardist Don Airey and then-former Deep Purple bassist Roger Glover—and this line-up gave the band their commercial breakthrough with the single "Since You Been Gone". Over the years Rainbow went through many personnel changes, with each studio album recorded with a different lineup, and leaving Blackmore as the band's only constant member. The singers Joe Lynn Turner and Doogie White followed Bonnet, and numerous backing musicians have come and gone. In addition to Blackmore, Rainbow's current lineup includes Ronnie Romero on vocals, Jens Johansson on keyboards, Bob Nouveau on bass and David Keith on drums.
A pioneer of power metal, the band's early work primarily featured mystical lyrics with a neoclassical metal style, but went in a more streamlined, commercial direction following Dio's departure from the group.Rainbow were ranked No. 90 on VH1's 100 Greatest Artists of Hard Rock. The band have sold over 28 million records worldwide, with 1,420,000 copies in the UK.Rainbow flag (LGBT movement)
The rainbow flag, commonly known as the gay pride flag or LGBT pride flag, is a symbol of lesbian, gay, bisexual and transgender (LGBT) pride and LGBT social movements. Other older uses of rainbow flags include a symbol of peace. The colors reflect the diversity of the LGBT community, as the flag is often used as a symbol of gay pride during LGBT rights marches. While this use of the rainbow flag originated in Northern California’s San Francisco Bay Area, the flag is now used worldwide.
Originally devised by San Francisco artist Gilbert Baker, the design has undergone several revisions since its debut in 1978, first to remove colors then restore them based on availability of fabrics. The most common variant consists of six stripes: red, orange, yellow, green, blue, and violet. The flag is typically flown horizontally, with the red stripe on top, as it would be in a natural rainbow.Rainbow trout
The rainbow trout (Oncorhynchus mykiss) is a trout and species of salmonid native to cold-water tributaries of the Pacific Ocean in Asia and North America. The steelhead (sometimes called "steelhead trout") is an anadromous (sea-run) form of the coastal rainbow trout (O. m. irideus) or Columbia River redband trout (O. m. gairdneri) that usually returns to fresh water to spawn after living two to three years in the ocean. Freshwater forms that have been introduced into the Great Lakes and migrate into tributaries to spawn are also called steelhead.
Adult freshwater stream rainbow trout average between 1 and 5 lb (0.5 and 2.3 kg), while lake-dwelling and anadromous forms may reach 20 lb (9 kg). Coloration varies widely based on subspecies, forms and habitat. Adult fish are distinguished by a broad reddish stripe along the lateral line, from gills to the tail, which is most vivid in breeding males.
Wild-caught and hatchery-reared forms of this species have been transplanted and introduced for food or sport in at least 45 countries and every continent except Antarctica. Introductions to locations outside their native range in the United States (U.S.), Southern Europe, Australia, New Zealand and South America have damaged native fish species. Introduced populations may affect native species by preying on them, out-competing them, transmitting contagious diseases (such as whirling disease), or hybridizing with closely related species and subspecies, thus reducing genetic purity. The rainbow trout is included in the list of the top 100 globally invasive species. Nonetheless, other introductions into waters previously devoid of any fish species or with severely depleted stocks of native fish have created sport fisheries such as the Great Lakes and Wyoming's Firehole River.
Some local populations of specific subspecies, or in the case of steelhead, distinct population segments, are listed as either threatened or endangered under the Endangered Species Act. The steelhead is the official state fish of Washington.Ritchie Blackmore
Richard Hugh Blackmore (born 14 April 1945) is an English guitarist and songwriter. He was one of the founding members of Deep Purple in 1968, playing jam-style hard-rock music which mixed guitar riffs and organ sounds. During his solo career he established the heavy metal
band Rainbow, which fused baroque music influences and elements of hard rock. Rainbow steadily moved to catchy pop-style mainstream rock. Later in life, he formed the traditional folk rock project Blackmore's Night, transitioning to vocalist-centred sounds. As a member of Deep Purple, Blackmore was inducted into the Rock and Roll Hall of Fame in April 2016.Ronnie James Dio
Ronald James Padavona (July 10, 1942 - May 16, 2010) known professionally as Ronnie James Dio or simply Dio, was an American heavy metal singer-songwriter and composer. He fronted or founded numerous groups throughout his career, including Elf, Rainbow, Black Sabbath, Dio, and Heaven & Hell.
Dio was born in Portsmouth, New Hampshire, where his family resided for his father's service in the U.S. Army during World War II; they soon relocated to Cortland, New York. His music career began there in 1957 as part of the Vegas Kings (later Ronnie and the Rumblers). In 1967, he formed the rock band Elf, which became a regular opening act for Deep Purple. In 1975, Deep Purple guitarist Ritchie Blackmore founded the band Rainbow along with Dio, where he began a successful career releasing albums such as "Rising" (1976) and "Long Live Rock N' Roll" (1978). In 1979, Dio joined Black Sabbath as lead singer. He appeared in two studio albums of the band which met with success: "Heaven & Hell" (1980) and "Mob Rules" (1981). In 1982 he left the band to pursue a solo career, having two albums certified platinum by RIAA. In 2006 he founded the band Heaven & Hell with ex-bandmate Tony Iommi. Dio was diagnosed with stomach cancer in 2009, from which he died the following year.
Dio is regarded as one of the greatest and most influential heavy metal artists of all time. He is known for popularizing the "Metal Horns" hand gesture in metal culture and his medieval-themed song lyrics. Dio had a powerful, versatile vocal range and was capable of singing both hard rock and lighter ballads. He was awarded the "Metal Guru Award" by Classic Rock Magazine in 2006. He was also named the "Best Metal singer" at the Revolver Golden Gods Awards in 2010.Sinking of the Rainbow Warrior
The sinking of the Rainbow Warrior, codenamed Opération Satanique, was a bombing operation by the "action" branch of the French foreign intelligence services, the Direction générale de la sécurité extérieure (DGSE), carried out on 10 July 1985. During the operation, two operatives sank the flagship of the Greenpeace fleet, the Rainbow Warrior, at the Port of Auckland in New Zealand on its way to a protest against a planned French nuclear test in Moruroa. Fernando Pereira, a photographer, drowned on the sinking ship.
France initially denied responsibility, but two French agents were captured by New Zealand Police and charged with arson, conspiracy to commit arson, willful damage, and murder. As the truth came out, the scandal resulted in the resignation of the French Defence Minister Charles Hernu.
The two agents pleaded guilty to manslaughter and were sentenced to ten years in prison. They spent just over two years confined to the French island of Hao before being freed by the French government.Several political figures, including then New Zealand Prime Minister David Lange, have referred to the bombing as an act of terrorism or state-sponsored terrorism.The Dark Tower (series)
The Dark Tower is a series of eight books written by American author Stephen King that incorporate themes from multiple genres, including dark fantasy, science fantasy, horror, and Western. It describes a "gunslinger" and his quest toward a tower, the nature of which is both physical and metaphorical. The series, and its use of the Dark Tower, expands upon Stephen King's multiverse and in doing so, links together many of his other novels.
In addition to the eight novels of the series proper that comprise 4,250 pages, many of King's other books relate to the story, introducing concepts and characters that come into play as the series progresses.
The series was chiefly inspired by the poem "Childe Roland to the Dark Tower Came" by Robert Browning, whose full text was included in the final volume's appendix. In the preface to the revised 2003 edition of The Gunslinger, King also identifies The Lord of the Rings, Arthurian Legend, and The Good, the Bad and the Ugly as inspirations. He identifies Clint Eastwood's "Man with No Name" character as one of the major inspirations for the protagonist, Roland Deschain. King's style of location names in the series, such as Mid-World, and his development of a unique language abstract to our own (High Speech), are also influenced by J. R. R. Tolkien's work.
A film based on The Gunslinger and also serving as a sequel to the events of The Dark Tower due to the nature of said book's ending was released in August 2017.Stephen King saw The Dark Tower series as a first draft, initially planning to rewrite it to eliminate continuity errors. However, after revising The Gunslinger, "he is trying to decide how much he can rewrite."Tom Clancy's Rainbow Six
Tom Clancy's Rainbow Six is a media franchise created by American author Tom Clancy about a fictional international counter-terrorist unit called "Rainbow". The franchise began with Clancy's novel Rainbow Six, which was adapted into a series of tactical first-person shooter video games.Tom Clancy's Rainbow Six Siege
Tom Clancy's Rainbow Six Siege (often shortened to Rainbow Six Siege) is a tactical shooter video game developed by Ubisoft Montreal and published by Ubisoft. It was released worldwide for Microsoft Windows, PlayStation 4, and Xbox One on December 1, 2015. The game puts heavy emphasis on environmental destruction and cooperation between players. Each player assumes control of an attacker or a defender in different gameplay modes such as rescuing a hostage, defusing a bomb, and taking control of a capture point. The title has no campaign but features a series of short missions that can be played solo. These missions have a loose narrative, focusing on recruits going through training to prepare them for future encounters with the White Masks, a terrorist group that threatens the safety of the world.
It is an entry in the Tom Clancy's Rainbow Six series and the successor to Tom Clancy's Rainbow 6: Patriots, a tactical shooter that had a larger focus on narrative. However, Patriots was eventually cancelled due to its technical shortcomings, and the team decided to reboot the franchise. The team evaluated the core of the Rainbow Six franchise and believed that letting players impersonate the top counter-terrorist operatives around the world suited the game most. To create authentic siege situations, the team consulted actual counter-terrorism units and looked at real-life examples of sieges. Powered by AnvilNext 2.0, the game also utilizes Ubisoft's RealBlast technology to create destructible environments.
Announced at Electronic Entertainment Expo 2014, it received four nominations from Game Critics Awards including Best of Show. The game received an overall positive reception from critics, with praise mostly directed to the game's tense multiplayer and focus on tactics. However, the game was criticized for its progression system and its lack of content. Initial sales were weak, but the game's player base increased significantly as Ubisoft adopted a "games as a service" model for the game and subsequently released several packages of free downloadable content. The company partnered with ESL to make Siege an esports game. In June 2018, two and a half years after the game's initial launch, the game surpassed 40 million registered players across all platforms.Trout
Trout is the common name for a number of species of freshwater fish belonging to the genera Oncorhynchus, Salmo and Salvelinus, all of the subfamily Salmoninae of the family Salmonidae. The word trout is also used as part of the name of some non-salmonid fish such as Cynoscion nebulosus, the spotted seatrout or speckled trout.
Trout are closely related to salmon and char (or charr): species termed salmon and char occur in the same genera as do fish called trout (Oncorhynchus – Pacific salmon and trout, Salmo – Atlantic salmon and various trout, Salvelinus – char and trout).
Lake trout and most other trout live in freshwater lakes and rivers exclusively, while there are others, such as the steelhead, which can spend two or three years at sea before returning to fresh water to spawn (a habit more typical of salmon). Steelhead that live out their lives in fresh water are called rainbow trout. Arctic char and brook trout are part of the char family. Trout are an important food source for humans and wildlife, including brown bears, birds of prey such as eagles, and other animals. They are classified as oily fish.Winx Club
Winx Club is an Italian animated television series created, directed, and produced by Iginio Straffi. It is set in a magical universe inhabited by fairies, witches, and other mythical creatures. The show follows a fairy warrior named Bloom as she enrolls at the Alfea College to train and hone her skills. The series is presented in a style that combines Japanese anime with Western animation. Common themes in Winx Club include romantic relationships and the transition to adulthood, juxtaposed with magic elements and action sequences.
Iginio Straffi conceived the show's concept in the late 1990s after working in the comic book industry. While developing the series, Straffi drew inspiration from manga and the comics of Sergio Bonelli. He consulted with Italian fashion designers to create a futuristic clothing style for the characters. Straffi's company, Rainbow, animated a pilot episode in 2000 and started production on a full season in 2002. In exchange for broadcast rights, Rai Fiction financed 25% of the show's budget, and the series' first episode premiered on Rai 2 on January 28, 2004.
Winx Club employs a serial format—modeled after those of American teen dramas—that follows an ongoing storyline, with individual story arcs comprising each season. Initially, Straffi planned for the plot to last three seasons, but he decided to continue the story following the show's success. In 2010, Nickelodeon became a co-producer of Winx Club, and its parent company Viacom gained 30% ownership of Rainbow in 2011. Production on the fifth and sixth seasons was divided between Rainbow and Nickelodeon Animation Studio. To attract an American audience, Viacom assembled a voice cast of Nickelodeon actors (including Elizabeth Gillies and Ariana Grande), invested US$100 million in advertising the series, and inducted Winx Club into Nickelodeon's franchise of Nicktoons.The series has been a ratings success in Italy and on Nickelodeon networks internationally. By 2014, Winx Club had been broadcast in over 150 countries worldwide. The series has developed a following among comic and fashion fans, and its portrayal of gender roles has generated academic interest. Critic reviews of the series have called attention to its themes of empowerment and positive relationships, as well as to the perceived sexualization of the character designs. Three theatrical films based on the series have been released, and the first two received David di Donatello Award nominations. The franchise has spawned two spin-off series and various forms of licensed merchandise, including a comic book serial, platform video games, and lines of fashion dolls. A live-action adaptation of Winx Club aimed at young adults was announced in 2018.