849:. 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 believed to be 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.
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1656:. 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.
1465:), 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
451:. 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.)
97:
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the bow obtained from a point source, because the disk diameter of the sun (0.533°) cannot be neglected compared to the width of a rainbow (2.36°). Further red of the first supplementary rainbow overlaps the violet of the primary rainbow, so rather than the final colour being a variant of spectral violet, it is actually a purple. 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
792:
933:. 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
1245:, 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.
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1090:) rainbow were published. The quinary rainbow lies partially in the gap between the primary and secondary rainbows and is far fainter than even the secondary. In a laboratory setting, it is possible to create bows of much higher orders. Felix Billet (1808â1882) 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
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1405:(384â322 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."
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960:, 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
1521:(1267â1319), 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
1137:. 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.
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higher in the sky, with its centre as high above the horizon as the normal rainbow's centre is below it. Reflection bows are usually brightest when the sun is low because at that time its light is most strongly reflected from water surfaces. As the sun gets lower the normal and reflection bows are drawn closer together. Due to the combination of requirements, a reflection rainbow is rarely visible.
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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
1199:(ice pellets) instead of liquid water. As light passes through the sleet, the light is refracted causing the rare phenomena. These have been documented across United States with the earliest publicly documented and photographed sleetbow being seen in Richmond, Virginia on 21 December 2012. Just like regular rainbows, these can also come in various forms, with a
458:, and most of the light emerges 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.
1945:"Newton named seven colors in the spectrum: red, orange, yellow, green, blue, indigo, and violet. More commonly today we only speak of six major divisions, leaving out indigo. A careful reading of Newtonâs work indicates that the color he called indigo, we would normally call blue; his blue is then what we would name blue-green or cyan."
377:. 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.
209:). The initialism is sometimes referred to in reverse order, as VIBGYOR. More modernly, the rainbow is often divided into red, orange, yellow, green, cyan, blue and violet. The apparent discreteness of main colours is an artefact of human perception and the exact number of main colours is a somewhat arbitrary choice.
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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
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pointing at the sun with the observer at the tip. The base of the cone forms a circle at an angle of 40â42° 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
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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,
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Light rays enter a raindrop from one direction (typically a straight line from the Sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. The light leaving the rainbow is spread over a wide angle, with a maximum intensity at the angles 40.89â42°. (Note: Between 2 and 100%
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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.
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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
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The colour pattern of a rainbow is different from a spectrum, and the colours are less saturated. There is spectral smearing in a rainbow since, 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
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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
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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
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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 does not perfectly align with the ordinary rainbow, if seen at the same spot. Tiny plastic or
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may be produced where sunlight reflects off a body of water before reaching the raindrops, 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
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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
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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,
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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
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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
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rainbow. More internal reflections cause bows of higher ordersâtheoretically unto infinity. As more and more light is lost with each internal reflection, however, each subsequent bow becomes progressively dimmer and therefore increasingly difficult to spot. An additional challenge in observing the
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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
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The reason the returning light is most intense at about 42° is that this is a turning point â 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
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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
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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
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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
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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
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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
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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
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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
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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.
1954:"Ex quo clarissime apparet, lumina variorum colorum varia esset refrangibilitate : idque eo ordine, ut color ruber omnium minime refrangibilis sit, reliqui autem colores, aureus, flavus, viridis, cĂŚruleus, indicus, violaceus, gradatim & ex ordine magis magisque refrangibiles."
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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.
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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
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In Saudi Arabia and other similar-minded countries, authorities seize children's clothing (including hats, hair clips, pencil cases, etc.) and toys if they are rainbow-coloured, claiming that such can encourage homosexuality, and selling such items is illegal.
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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
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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.
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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
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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.
1502:(1031â1095) hypothesisedâas a certain Sun Sikong (1015â1076) did before himâthat 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
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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.
1529:), 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
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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
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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
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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
443:. 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
1275:, 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
115:. 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
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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.
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1597:) 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.
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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.
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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
1774:'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. In
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70:. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne
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Tertiary and quaternary rainbows should not be confused with "triple" and "quadruple" rainbowsâterms sometimes erroneously used to refer to the (much more common) supernumerary bows and reflection rainbows.
427:. Seawater has a higher refractive index than rain water, so the radius of a "rainbow" in sea spray is smaller than that of a true rainbow. This is visible to the naked eye by a misalignment of these bows.
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about 10° outside it at an apparent angle of 50â53°. 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.
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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
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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
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Nader El-Bizri 'Ibn al-Haytham et le problème de la couleur', Oriens-Occidens: Cahiers du centre d'histoire des sciences et des philosophies arabes et mĂŠdiĂŠvales, C.N.R.S. 7 (2009), pp. 201â226.
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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).
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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.
240:, 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
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Double rainbow and supernumerary rainbows on the inside of the primary arc. The shadow of the photographer's head at the bottom of the photograph marks the centre of the rainbow circle (the
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regions, however, these bands are not visible to humans. Only near frequencies of these regions to the visible spectrum are included in rainbows, since water and air become increasingly
77:
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.
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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
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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
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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.
1620:, 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
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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.
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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
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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
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of the light is reflected at each of the three surfaces encountered, depending on the angle of incidence. This diagram only shows the paths relevant to the rainbow.)
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example in an aeroplane (see below). Alternatively, an observer with the right vantage point may see the full circle in a fountain or waterfall spray.
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1078:) 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.
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are two related optical phenomena similar in appearance to a rainbow, but unlike the latter, their origin lies in light refraction through hexagonal
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889:, which is much smaller in diameter and is created by different optical processes. In the right circumstances, a glory and a (circular) rainbow or
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White light separates into different colours on entering the raindrop due to dispersion, causing red light to be refracted less than blue light.
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Newton, who admitted his eyes were not very critical in distinguishing colours, originally (1672) divided the spectrum into five main colours:
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is the personification of the rainbow, a messenger goddess who, like the rainbow, connects the mortal world with the gods through messages.
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4943:â Description of multiple types of bows, including: "bows that cross, red bows, twinned bows, coloured fringes, dark bands, spokes", etc.
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circle normally seen is about 50% during sunset or sunrise. Viewing the rainbow's lower half requires the presence of water droplets
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through and the sun is fairly bright. They are very largeâalmost as big as a rainbow and much broader. They sometimes appear with a
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in 1908. Advances in computational methods and optical theory continue to lead to a fuller understanding of rainbows. For example,
1179:, which are very common around the world and visible much more often than rainbows (of any order), yet are unrelated to rainbows.
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is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames.
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Sadeghi, Iman; Munoz, Adolfo; Laven, Philip; Jarosz, Wojciech; Seron, Francisco; Gutierrez, Diego; Jensen, Henrik Wann (2012).
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GroĂmann, Michael; Schmidt, Elmar; HauĂmann, Alexander (1 October 2011). "Photographic evidence for the third-order rainbow".
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between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in
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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
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corpuscular theory of light was unable to explain supernumerary rainbows, and a satisfactory explanation was not found until
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A sleetbow forms in the same way as a typical rainbow, with the exception that it occurs when light passes through falling
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A "normal" secondary rainbow may be present as well. Twinned rainbows can look similar to, but should not be confused with
251:, and the days of the week. Scholars have noted that what Newton regarded at the time as "blue" would today be regarded as
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Experiments on the rainbow phenomenon using artificial raindrops, i.e. water-filled spherical flasks, go back at least to
1439:; he favours the latter. He also discusses other phenomena related to rainbows: the mysterious "virgae" (rods), halos and
724:{\displaystyle \beta _{\text{max}}=\arccos \left({\frac {2{\sqrt {-1+n^{2}}}}{{\sqrt {3}}n}}\right)\approx 40.2^{\circ }.}
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when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.
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Isaac Newton demonstrated that white light was composed of the light of all the colours of the rainbow, which a glass
1098:. Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam.
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but also at other museums. The book is divided into seven sections, each coloured a different colour of the rainbow.)
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to these frequencies, scattering the light. The UV band is sometimes visible to cameras using black and white film.
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1517:(1236â1311), gave a fairly accurate explanation for the rainbow phenomenon. This was elaborated on by his student,
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When sunlight encounters a raindrop, part of the light is reflected and the rest enters the raindrop. The light is
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1963:"approximation obtained by his model was good enough to allow him to ignore the effects of the glass container."
956:, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through
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Meanwhile, the even rarer case of a rainbow split into three branches was observed and photographed in nature.
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J.D. Walker, "Mysteries of rainbows, notably their rare supernumerary arcs," Sci. Am. 242(6), 174â184 (1980).
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rather than liquid water droplets. This means that they are not rainbows, but members of the large family of
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It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an
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Ng, P. H.; Tse, M. Y.; Lee, W. K. (1998). "Observation of high-order rainbows formed by a pendant drop".
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4395:âRainbow: Refraction of white light by a liquid sphere.â, U.C. Berkeley Physics Lecture Demonstrations,
1714:, where it is a sign of God's covenant to never destroy all life on Earth with a global flood again. In
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can occur together. Another atmospheric phenomenon that may be mistaken for a "circular rainbow" is the
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1805:) with the ends resting on clouds. Generalised examples in coat of arms include those of the towns of
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247:, who thought there was a connection between the colours, the musical notes, the known objects in the
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953:
455:
435:(brightness) of the bow would tend toward infinity at this angle if interference effects are ignored
3549:
2926:
1457:(965â1039 AD) attempted to provide a scientific explanation for the rainbow phenomenon. In his
1211:
5832:
5822:
5817:
5812:
5295:
5028:
4960:
3948:
1606:
965:
957:
825:
17:
4970:â video explanation of basics, shown artificial rainbow at night, second rainbow and circular one.
4918:
4314:
3409:
Theusner, Michael (1 October 2011). "Photographic observation of a natural fourth-order rainbow".
2081:
5879:
5837:
3379:
2880:
1832:
4050:
6053:
6043:
5060:
4517:
3898:
2921:
1848:
1514:
1503:
1262:
1191:
Monochrome sleetbow captured during the early morning on 7 January 2016 in
Valparaiso, Indiana.
177:
5235:
4293:
4269:
4077:
3921:
3691:
2800:
2243:
2161:
Optice: Sive de
Reflexionibus, Refractionibus, Inflexionibus & Coloribus Lucis Libri Tres,
1985:
1435:
each water drop, the other, that it is produced by the Sun reflected in a cloud shaped like a
820:
secondary. The dark area of unlit sky lying between the primary and secondary bows is called
5761:
5516:
5417:
5405:
4981:
4478:
G. Casini and A. Covello, âThe ârainbowâ in the drop,â Am. J. Phys. 80(11), 1027â1034 (2012).
3733:
2505:
2023:
1871:
logo. Many political alliances spanning multiple political parties have called themselves a "
1840:
1703:
1676:
1649:
1563:
1478:
1473:, and, though incorrect, provided the groundwork for the correct explanations later given by
1410:
1276:
901:
rather than liquid water droplets, and is located around the Sun (or Moon), not opposite it.
807:
A secondary rainbow, at a greater angle than the primary rainbow, is often visible. The term
505:, then the angle of incidence of the Sun's rays with respect to the drop's surface normal is
374:
3824:
3148:
2506:"Color categories are not universal: Replications and new evidence from a stone-age culture"
5734:
4927:
4351:
4281:
4202:
3620:
3561:
3418:
3329:
2853:
2355:
1901:
1284:
1249:
4760:. Berkeley, California: Shambhala Publications and The Fine Arts Museums of San Francisco.
4026:
China's Major
Mysteries: Paranormal Phenomena and the Unexplained in the People's Republic
2645:
2210:
8:
5864:
5549:
5449:
5381:
5270:
5072:
4437:âRevisiting the round bottom flask rainbow experiment.â, M. Selmke and S. Selmke, arXiv,
1911:
1844:
1822:
1672:
1617:
1583:
821:
796:
791:
448:
96:
59:
55:
4487:âPrimary and Secondary Bow of a Rainbowâ, U.C. Berkeley Physics Lecture Demonstrations,
4355:
4324:(Contributions to the optics of turbid media, especially of colloidal metal solutions),
4294:"Supplement to a paper, "On the intensity of light in the neighbourhood of a caustic," "
4285:
4206:
3624:
3565:
3422:
3333:
2857:
1706:, and have been used in the arts. The first literary occurrence of a rainbow is in the
5278:
5230:
5178:
5163:
5158:
5136:
5065:
4875:
4867:
4844:
4775:
4738:
4643:
4363:
4171:
4123:
3573:
3450:
3361:
2939:
2391:
2183:
1896:
1891:
1546:
1495:
1426:
1223:
1216:
1200:
1015:
488:
It is possible to determine the perceived angle which the rainbow subtends as follows.
127:, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human
47:
4673:
1347:
194:
For colours seen by the human eye, the most commonly cited and remembered sequence is
66:
of light appearing in the sky. The rainbow takes the form of a multicoloured circular
5974:
5927:
5655:
5524:
5422:
5339:
5300:
5217:
5173:
4898:
4879:
4854:
4831:
4812:
4785:
4742:
4716:
4647:
4521:
4460:
4459:
Pictures and
Raytracings under "Alexander's dark band (or bright band?)", M. Selmke,
4220:
4175:
4127:
4103:
4083:
4029:
3927:
3442:
3434:
3353:
3345:
2869:
2841:
2528:
2471:
2463:
2249:
2187:
1991:
1692:
1227:
128:
3454:
1743:
1578:
1151:
198:'s sevenfold red, orange, yellow, green, blue, indigo and violet, remembered by the
6033:
5922:
5917:
5897:
5892:
5477:
5250:
5245:
5225:
5183:
5141:
5119:
5043:
4869:
4635:
4359:
4210:
4163:
4115:
3628:
3569:
3525:
3426:
3337:
2943:
2931:
2861:
2520:
2455:
2129:
1779:
1759:
438:
424:
101:
63:
4948:
4011:
Science in
Ancient China: Researches and Reflections Brookfield, Vermont: VARIORUM
3365:
3228:
3127:
2760:
2728:
2301:
1831:
have been used for centuries. It was a symbol of the
Cooperative movement in the
916:
photograph of a rainbow with additional supernumerary bands inside the primary bow
836:
5952:
5942:
5937:
5902:
5804:
5640:
5587:
5504:
5499:
5410:
5305:
4850:
4767:
4639:
4551:
4511:
4495:
4467:
4445:
4422:
4403:
4384:
4321:
3873:
3720:
3685:
3654:
3109:
2891:
2386:
1802:
1775:
1715:
1707:
1696:
1390:
1156:
1116:
233:
151:
143:
35:
4415:
3847:
3678:
3284:
3175:
3160:
3091:
2588:
2524:
2278:
6002:
5947:
5932:
5912:
5907:
5690:
5472:
5358:
5327:
5283:
5240:
5112:
5077:
5050:
3953:. Vol. Book I (Delphi Ancient Classics Book 27 ed.). Delphi Classics.
3302:
2815:
1864:
1856:
1653:
1621:
1601:
1594:
1483:
1454:
1436:
1331:
1305:
1121:
523:
491:
Given a spherical raindrop, and defining the perceived angle of the rainbow as
463:
241:
229:
189:
67:
4967:
4892:
3149:"Bakerian Lecture: Experiments and calculations relative to physical optics,"
2614:
2107:
373:
of whether everyone sees seven colours in a rainbow is related to the idea of
6027:
5887:
5685:
5467:
5459:
5392:
5260:
5200:
5124:
5107:
5013:
4224:
4191:"Did Kepler's Supplement to Witelo Inspire Descartes' Theory of the Rainbow?"
3438:
3349:
2799:(University Park, Pennsylvania: Pennsylvania State University Press, 2001),
2467:
2443:
1798:
949:
431:
42°. If the Sun were a laser emitting parallel, monochromatic rays, then the
135:
4564:
4488:
4106:(Summer 1966). "Roger Bacon's Theory of the Rainbow: Progress or Regress?".
3632:
2935:
1867:. The rainbow has also been used in technology product logos, including the
1814:
1006:
above the horizon (5, 6) with their reflected counterparts below it (7, 8).
909:
390:
5859:
5722:
5678:
5494:
5489:
5484:
5400:
5353:
5322:
5255:
5099:
4619:
4507:
4396:
3446:
3357:
3197:
2873:
2532:
2335:
1852:
1828:
1767:
1682:
1491:
1422:
1272:
1231:
898:
354:
Moreover, rainbows have bands beyond red and violet in the respective near
248:
195:
147:
131:
for colour is poor in low light, moonbows are often perceived to be white.
3794:
3051:
2475:
1652:
in the 14th century. Later, also
Descartes studied the phenomenon using a
161:
From above the Earth such as in an aeroplane, it is sometimes possible to
5717:
5540:
5444:
5288:
5193:
5151:
5146:
5089:
5055:
4956:
3763:
3430:
3341:
3319:
2865:
2211:"Understand the science of appearance of different colors of the rainbow"
1550:
1196:
799:
visible between the primary and secondary bows. Also note the pronounced
359:
30:
3490:
1987:
The
Rainbow Sky: An Exploration of Colors in the Solar System and Beyond
1687:
1609:
realised that light behaves as a wave under certain conditions, and can
1574:
RenĂŠ Descartes's sketch of how primary and secondary rainbows are formed
894:
5869:
5712:
5432:
5188:
5129:
4808:
4730:
4376:âFlorence's Rainbowâ, Harvard Natural Sciences Lecture Demonstrations,
1868:
1836:
1771:
1625:
1590:
1556:
1466:
1091:
444:
419:
107:
Rainbows can be observed whenever there are water drops in the air and
51:
4315:"Beiträge zur Optik trßber Medien, speziell kolloidaler MetallÜsungen"
3550:"How to create and observe a dozen rainbows in a single drop of water"
3530:
3513:
3073:
3025:
2973:"Triple-split rainbow observed and photographed in Japan, August 2012"
1719:
169:
phenomenon, but a glory is usually much smaller, covering only 5â20°.
5729:
5702:
5697:
5206:
4937:
2459:
1860:
1731:
1402:
1299:
A first order rainbow from water (left) and a sugar solution (right).
1020:
940:
Supernumerary rainbows cannot be explained using classical geometric
929:; together with the rainbow itself the phenomenon is also known as a
432:
180:
tangential to the arc. The light of the second arc is 90% polarised.
81:
4868:
Minnaert, Marcel G.J.; Lynch, David K.; Livingston, William (1973).
4845:
Minnaert, Marcel G.J.; Lynch, David K.; Livingston, William (1993).
3713:
1570:
1203:
sleetbow being documented on 7 January 2016 in
Valparaiso, Indiana.
978:
5984:
5707:
5315:
4933:
Rainbow seen through infrared filter and through ultraviolet filter
4438:
4167:
4119:
3254:
1878:
Pointing at rainbows has been considered a taboo in many cultures.
1786:
1763:
1739:
1530:
1499:
1470:
1451:
1280:
860:
604:
355:
199:
155:
139:
108:
5372:
4928:
Interactive simulation of light refraction in a drop (java applet)
4825:
4674:"Saudi authorities seize rainbow toys for promoting homosexuality"
4154:
Boyer, Carl B. (1952). "Descartes and the Radius of the Rainbow".
1644:
Round bottom flask rainbow demonstration experiment - Johnson 1882
480:
5756:
4798:
4237:
3968:
2339:
2078:"Lunar Rainbows â When to View and How to Photograph a "Moonbow""
1926:
1921:
1916:
1810:
1755:
1723:
1440:
1431:
1314:
1283:
rainbows may be more common, but an observer would need infrared
1146:
1133:
1111:
1082:
photographed as well, and in 2014 the first ever pictures of the
890:
244:
206:
124:
4973:
4075:
3919:
3052:"APOD: 2014 September 30 â A Full Circle Rainbow over Australia"
2842:"Observation, analysis, and reconstruction of a twinned rainbow"
764:), the radius angle is 42.5°; for blue light (wavelength 350nm,
5979:
5582:
5572:
4028:. San Francisco: China Books and Periodicals, Inc. p. 72.
3469:"Short Sharp Science: First ever image of fourth-order rainbow"
2561:
2504:
Roberson, Debi; Davies, Ian; Davidoff, Jules (September 2000).
2104:"Why is the inside of a rainbow brighter than the outside sky?"
1790:
1735:
1727:
1268:
1242:
941:
363:
237:
217:
183:
150:
of 19 mm or less would be required. Now that software for
2999:"Can you ever see the whole circle of a rainbow? | Earth"
2179:
Introduction to Light: The Physics of Light, Vision, and Color
982:
Reflection rainbow (top) and normal rainbow (bottom) at sunset
5607:
5602:
5592:
5562:
5033:
5004:
4270:"On the intensity of light in the neighbourhood of a caustic"
1806:
1794:
1751:
1481:(c. 1250âc. 1311)âboth having studied al-Haytham's
1241:
Both arcs are brightly coloured ring segments centred on the
1095:
221:
116:
4342:
Nussenzveig, H. Moyses (1977). "The Theory of the Rainbow".
2881:"Researchers unlock secret of the rare 'twinned rainbow,' "
1506:"is basically in accord with modern scientific principles."
1187:
255:, and what Newton called "indigo" would today be considered
5597:
5577:
5557:
5427:
5344:
4893:
Naylor, John; Lynch, David K.; Livingston, William (2002).
4216:
10.1175/1520-0477(1989)070<0750:DKSTWI>2.0.CO;2
3207:
3173:
1747:
1711:
1663:
Other experiments use small liquid drops (see text above).
1206:
964:
nature of light, and the first explanation was provided by
961:
468:
405:
256:
252:
225:
4595:"How Did the Rainbow Flag Become a Symbol of LGBTQ Pride?"
4433:
4431:
3899:"The Internet Classics Archive â Meteorology by Aristotle"
2491:
The ancestor's tale: a pilgrimage to the dawn of evolution
5673:
5567:
5332:
3950:
Delphi Complete Works of Seneca the Younger (Illustrated)
3514:"MĂŠmoire sur les Dix-neuf premiers arcs-en-ciel de l'eau"
3152:
Philosophical Transactions of the Royal Society of London
2302:"Music For Measure: On the 300th Anniversary of Newton's
213:
71:
4513:
Secret of the Vajra World: The Tantric Buddhism of Tibet
971:
4428:
2904:
2652:. The Board of Trustees at the University of Illinois.
454:
The light at the back of the raindrop does not undergo
4762:(Large format handbook for the Summer 1976 exhibition
4341:
4079:
The rainbow bridge: rainbows in art, myth, and science
3923:
The rainbow bridge: rainbows in art, myth, and science
2797:
The Rainbow Bridge: Rainbows in Art, Myth, and Science
2503:
1990:. Springer Science & Business Media. p. 200.
4801:
The Rainbow Bridge: Rainbows in Art, Myth and Science
4455:
4453:
3196:
Nemiroff, R.; Bonnell, J., eds. (12 September 2007).
1350:
784:"Double rainbow" redirects here. For other uses, see
633:
62:
of light in water droplets resulting in a continuous
3714:
Observing Halos â Getting Started Atmospheric Optics
1789:, the rainbow proper consists of 4 bands of colour (
1290:
351:, it is the number of main colours in the spectrum.
4297:
Transactions of the Cambridge Philosophical Society
4274:
Transactions of the Cambridge Philosophical Society
3518:
Annales Scientifiques de l'Ăcole Normale SupĂŠrieure
3229:"Atmospheric Optics: Reflection rainbows formation"
1344:times internally reflected rays escapes the domain
1267:It has been suggested that rainbows might exist on
885:A circular rainbow should not be confused with the
5626:Linguistic relativity and the colour naming debate
4450:
3786:
2676:"How to see a whole circle rainbow â EarthSky.org"
1847:and the June pride month since it was designed by
1375:
723:
4799:Lee, Raymond L. & Alastair B. Fraser (2001).
4624:"Pointing, Rainbows, and the Archaeology of Mind"
4144:(On the rainbow and the impressions of radiance).
4102:
3969:O'Connor, J.J.; Robertson, E.F. (November 1999).
3516:[Memoir on the first nineteen rainbows].
2753:
2446:(1972). "Universals in color naming and memory".
1253:missed since it occurs almost directly overhead.
6025:
4238:O'Connor, J.J.; Robertson, E.F. (January 2000).
734:Substituting back into the earlier equation for
4195:Bulletin of the American Meteorological Society
3195:
2606:
2248:. University of California Press. p. 140.
1835:in the 16th century, of peace in Italy, and of
1469:verification. This explanation was repeated by
1304:glass marbles may be used in road marking as a
1024:Unenhanced photo of a red (monochrome) rainbow
559:is the refractive index of water. Solving for
498:, and the angle of the internal reflection as
447:, and hence its colour. This effect is called
4989:
4895:Out of the Blue: A 24-Hour Skywatcher's Guide
4871:The Nature of Light and Color in the Open Air
4826:Lynch, David K.; Livingston, William (2001).
4008:
3971:"Kamal al-Din Abu'l Hasan Muhammad Al-Farisi"
3597:
3595:
3543:
3541:
2205:
2203:
2171:
2169:
2163:Propositio II, Experimentum VII, edition 1740
4830:(2nd ed.). Cambridge University Press.
3023:
3017:
2734:. Harvard University Department of Physics.
2442:
2348:
2182:(2002 revised ed.). Mineola, New York:
2155:
2153:
2151:
1256:
944:. The alternating faint bands are caused by
184:Number of colours in a spectrum or a rainbow
4076:Raymond L. Lee; Alistair B. Fraser (2001).
3964:
3962:
3960:
3920:Raymond L. Lee; Alistair B. Fraser (2001).
3613:Journal of the Optical Society of America B
3382:Triple Rainbows Exist, Photo Evidence Shows
3161:Atmospheric Optics: Supernumerary Rainbows
2513:Journal of Experimental Psychology: General
1746:were over the people thanked him, offering
1554:
1164:
1105:
879:
846:
800:
165:. This phenomenon can be confused with the
6008:
4996:
4982:
4472:
4023:
3592:
3538:
2200:
2166:
1983:
750:â 42° as the radius angle of the rainbow.
475:
176:The light of a primary rainbow arc is 96%
111:shining from behind the observer at a low
4481:
4389:
4214:
4188:
3529:
2925:
2907:"Physically-based simulation of rainbows"
2698:"USATODAY.com â Look down on the rainbow"
2646:"Why are rainbows curved as semicircles?"
2299:
2148:
2080:. The Ansel Adams Gallery. Archived from
1710:chapter 9, as part of the flood story of
1616:Young's work was refined in the 1820s by
1215:A circumhorizontal arc (bottom), below a
904:
5777:International Commission on Illumination
4773:
4048:
3957:
3818:
3610:
3408:
2991:
2839:
1686:
1666:
1639:
1593:(subsequently to, but independently of,
1569:
1446:According to HĂźseyin Gazi Topdemir, the
1294:
1210:
1207:Circumhorizontal and circumzenithal arcs
1186:
1150:
1115:
1039:
1019:
977:
908:
859:
835:
790:
479:
162:
120:rainbow, with inverse order of colours.
95:
29:
4729:
4408:
4370:
3975:MacTutor History of Mathematics archive
3871:
3845:
3792:
2795:Raymond L. Lee and Alistair B. Fraser,
2612:
2586:
2488:
2175:
2075:
2052:
591:The rainbow will occur where the angle
6026:
5767:Color Association of the United States
4968:Creating Circular and Double Rainbows!
4946:
4755:
4049:Davidson, Michael W. (1 August 2003).
4013:. III: Ashgate Publishing. p. 24.
3947:Seneca, Lucius Anneus (1 April 2014).
3946:
3909:from the original on 18 February 2014.
3547:
3511:
3235:from the original on 23 September 2015
3110:"Supernumerary Rainbows and drop size"
2816:"Atmospheric Optics: Twinned rainbows"
2334:
1845:rainbow flag as a symbol of LGBT pride
855:
205:or as the name of a fictional person (
4977:
4709:The Rainbow, From Myth to Mathematics
4706:
4684:from the original on 7 September 2022
4654:from the original on 18 November 2021
4618:
4153:
4142:De iride et radialibus impressionibus
4140:Theodoric of Freiberg (c. 1304â1310)
3491:"Observations of the quinary rainbow"
3062:from the original on 25 January 2015.
2840:HauĂmann, Alexander (February 2015).
2136:from the original on 9 September 2013
2061:. The Weather Company. Archived from
1549:. His work on light was continued by
1396:
1175:Fog bows should not be confused with
1009:
972:Reflected rainbow, reflection rainbow
597:is maximum with respect to the angle
4592:
4575:from the original on 21 October 2019
4267:
3774:from the original on 26 January 2021
3744:from the original on 28 October 2021
3501:from the original on 3 January 2015.
3386:. Sciencedaily.com. 6 October 2011.
3265:from the original on 4 February 2015
2786:Commentary on Book IV of Aristotle's
2782:Commentary on Book IV of Aristotle's
2726:
2708:from the original on 12 October 2013
2686:from the original on 4 October 2013.
2643:
2625:from the original on 13 January 2013
2316:from the original on 18 January 2017
2241:
1053:rainbow; two reflections create the
875:
203:Richard Of York Gave Battle In Vain,
4805:Pennsylvania State University Press
4506:
4057:from the original on 30 August 2006
3580:from the original on 14 August 2011
3390:from the original on 4 October 2013
3032:from the original on 5 October 2013
3005:from the original on 4 October 2013
2975:. blog.meteoros.de. 12 March 2015.
2741:from the original on 8 October 2016
2656:from the original on 2 October 2015
2568:from the original on 18 August 2013
2268:
2223:from the original on 10 August 2020
1734:was the god of the rainbow for the
1383:. This results in a rainbow of the
516:. Since the angle of refraction is
13:
5631:Blueâgreen distinction in language
4766:which took place primarily at the
4700:
4364:10.1038/scientificamerican0477-116
3981:from the original on 25 March 2007
3574:10.1038/scientificamerican0777-138
3479:from the original on 11 July 2017.
3255:"Dawn Red Rainbows Arizona â OPOD"
2953:from the original on 12 March 2020
2448:Journal of Experimental Psychology
2384:
1912:Iridescent colours in soap bubbles
1742:and when the regular rains on the
831:
779:
14:
6070:
5003:
4912:
4246:from the original on 10 June 2007
4189:Gedzelman, Stanley David (1989).
4082:. Penn State Press. p. 156.
3926:. Penn State Press. p. 109.
3384:, ScienceDaily.com, Oct. 5, 2011"
3174:Les Cowley (Atmospheric Optics).
2979:from the original on 2 April 2015
2366:from the original on 10 June 2021
2106:. WeatherQuesting. Archived from
2004:from the original on 22 June 2023
1819:69th Infantry Regiment (New York)
1509:According to Nader El-Bizri, the
1291:Rainbows with different materials
952:, reinforcing each other through
840:The primary rainbow is "twinned."
753:For red light (wavelength 750nm,
6007:
5998:
5997:
5788:International Colour Association
5371:
3157:: 1â16; see especially pp. 8â11.
2424:from the original on 1 June 2023
2034:from the original on 20 May 2023
1859:described newly democratic post-
762:the dispersion relation of water
404:
389:
5783:International Colour Consortium
4847:Light and Color in the Outdoors
4756:Graham, Lanier F., ed. (1976).
4666:
4612:
4586:
4557:
4534:
4500:
4335:
4307:
4258:
4231:
4182:
4147:
4134:
4096:
4069:
4042:
4017:
4002:
3993:
3940:
3913:
3891:
3865:
3839:
3812:
3756:
3726:
3706:
3669:
3639:
3604:
3505:
3483:
3461:
3402:
3372:
3313:
3295:
3277:
3247:
3221:
3189:
3167:
3138:
3120:
3102:
3084:
3066:
3044:
2965:
2898:
2830:
2808:
2771:
2720:
2690:
2668:
2637:
2580:
2554:
2542:from the original on 9 May 2020
2497:
2482:
2436:
2406:
2378:
2328:
2293:
2262:
2235:
2053:Masters, Jeff (14 April 2005).
1957:
1948:
1813:, both in Bavaria, Germany; of
1477:in 1309 and, independently, by
1459:Maqala fi al-Hala wa Qaws Quzah
1155:Fogbow and glory, as well as a
5848:List of Crayola crayon colours
5772:International Colour Authority
4897:. Cambridge University Press.
3303:"3rd & 4th order rainbows"
3024:Philip Laven (4 August 2012).
3001:. EarthSky. 15 December 2012.
2792:Meteorology 4), commentary 41.
2356:"WATCH: This Is Not a Rainbow"
2122:
2096:
2069:
2046:
2016:
1977:
1939:
1635:
1370:
1351:
771:), the radius angle is 40.6°.
380:
163:see a rainbow as a full circle
1:
6039:Atmospheric optical phenomena
4923:American mathematical society
4242:. University of St. Andrews.
2818:. Atoptics.co.uk. 3 June 2002
2784:Meteorology (also known as:
2729:"Solution, Week 81, Rainbows"
2130:"Rainbow â A polarized arch?"
1970:
1851:in 1978. In 1994, Archbishop
1726:) and the realm of the gods (
1415:
774:
347:is used inaccurately to mean
91:
5651:Traditional colours of Japan
5428:Achromatic colours (Neutral)
5311:Multi-primary colour display
4777:Rainbows, Halos, and Glories
4640:10.5771/0257-9774-2021-1-145
4414:âThe Rainbow,âJ.B. Calvert,
4053:. Florida State University.
3977:, University of St Andrews.
3203:Astronomy Picture of the Day
3198:"Six Rainbows Across Norway"
3128:"Fogbow droplet size effect"
2914:ACM Transactions on Graphics
1632:provides a modern overview.
1537:In Europe, Ibn al-Haytham's
1401:The classical Greek scholar
7:
5085:Spectral power distribution
4919:The Mathematics of Rainbows
4425:, Retrieved 10 January 2016
3723:, accessed 3 December 2013.
2525:10.1037/0096-3445.129.3.369
1885:
1722:connects the world of men (
1389:-th order shrinking to the
1182:
1120:Spray moonbow at the Lower
934:
436:
10:
6075:
5511:Colour realism (art style)
5169:Evolution of colour vision
4782:Cambridge University Press
4713:Princeton University Press
3679:Atmospheric Optics: Fogbow
2780:Alexander of Aphrodisias,
2076:Walklet, Keith S. (2006).
1907:Glory (optical phenomenon)
1702:Rainbows occur frequently
1680:
1670:
1527:The Revision of the Optics
1260:
1144:
1109:
1013:
828:, who first described it.
783:
187:
15:
5993:
5965:
5878:
5828:List of colours (compact)
5803:
5796:
5747:
5666:
5646:Colour in Chinese culture
5616:
5548:
5539:
5458:
5391:
5380:
5369:
5269:
5216:
5098:
5021:
5012:
4828:Color and Light in Nature
4774:Greenler, Robert (1980).
4051:"Roger Bacon (1214â1294)"
3734:"Friday Night â Sleetbow"
3692:"The theory of fog-bows,"
3690:James C. McConnel (1890)
3647:"Moonbow â Lunar Rainbow"
2489:Dawkins, Richard (2005).
2387:"Primary rainbow colours"
2300:Hutchison, Niels (2004).
1257:Extraterrestrial rainbows
1140:
954:constructive interference
456:total internal reflection
25:Meteorological phenomenon
5833:List of colours by shade
5296:Digital image processing
5029:Electromagnetic spectrum
4961:University of Nottingham
4550:14 February 2023 at the
3092:"Supernumerary Rainbows"
2644:Anon (7 November 2014).
2055:"The 360-degree Rainbow"
1932:
1106:Rainbows under moonlight
958:destructive interference
826:Alexander of Aphrodisias
315:Modern reinterpretation
18:Rainbow (disambiguation)
5838:List of colour palettes
4707:Boyer, Carl B. (1987).
4599:Encyclopedia Britannica
3633:10.1364/JOSAB.15.002782
3560:(July): 138â144 + 154.
2936:10.1145/2077341.2077344
2702:usatoday30.usatoday.com
2216:EncyclopĂŚdia Britannica
1523:Kitab Tanqih al-Manazir
1494:(960â1279), a polymath
1463:On the Rainbow and Halo
905:Supernumerary rainbows
803:inside the primary bow.
484:Mathematical derivation
476:Mathematical derivation
289:Newton's later colours
265:Newton's first colours
100:A colorful rainbow and
5061:Structural colouration
4518:Shambhala Publications
4494:8 January 2017 at the
4466:8 January 2017 at the
4444:8 January 2017 at the
4402:8 January 2017 at the
4383:8 January 2017 at the
4009:Sivin, Nathan (1995).
3795:"Circumhorizontal arc"
3695:Philosophical Magazine
3548:Walker, Jearl (1977).
3512:Billet, Felix (1868).
2727:Anon (29 March 2004).
2176:Waldman, Gary (1983).
1699:
1695:of the rainbow in the
1645:
1575:
1555:
1519:KamÄl al-DÄŤn al-FÄrisÄŤ
1515:Qutb al-Din al-Shirazi
1504:atmospheric refraction
1475:KamÄl al-DÄŤn al-FÄrisÄŤ
1377:
1300:
1263:Extraterrestrial skies
1219:
1192:
1159:
1124:
1025:
983:
923:supernumerary rainbows
917:
865:
841:
804:
725:
485:
154:several images into a
104:
39:
5843:List of colour spaces
5762:Color Marketing Group
5517:On Vision and Colours
5450:Tinctures in heraldry
5433:Polychromatic colours
5418:Complementary colours
5406:Monochromatic colours
4947:Merrifield, Michael.
4941:website by Les Cowley
3495:www.weatherscapes.com
3074:"OPOD â 360° Rainbow"
2890:9 August 2012 at the
2444:Rosch Heider, Eleanor
2275:SHiPS Resource Center
1841:LGBT social movements
1821:of the United States
1817:, France; and of the
1718:, the rainbow bridge
1690:
1677:Rainbows in mythology
1667:Culture and mythology
1650:Theodoric of Freiberg
1643:
1573:
1564:Theodoric of Freiberg
1543:translated into Latin
1479:Theodoric of Freiberg
1411:Naturales Quaestiones
1378:
1298:
1228:circumhorizontal arcs
1214:
1190:
1172:at the bow's centre.
1154:
1119:
1040:Higher-order rainbows
1023:
981:
912:
897:, which is caused by
863:
839:
794:
726:
483:
375:linguistic relativity
99:
33:
6059:Atmospheric sciences
5823:List of colours: NâZ
5818:List of colours: GâM
5813:List of colours: AâF
5735:Tint, shade and tone
5618:Cultural differences
4764:The Rainbow Art Show
4320:2 March 2012 at the
4268:Airy, G. B. (1838).
3827:on 21 September 2008
3764:"Circumzenithal Arc"
3740:. 22 December 2012.
3684:15 June 2022 at the
3473:www.newscientist.com
3431:10.1364/AO.50.00F129
3342:10.1364/AO.50.00F134
3309:. 16 September 2023.
3291:. 16 September 2023.
3147:Thomas Young (1804)
3134:. 16 September 2023.
3116:. 16 September 2023.
3098:. 16 September 2023.
3080:. 16 September 2023.
2866:10.1364/AO.54.00B117
2788:De Meteorologica or
2767:. 16 September 2023.
2418:scienceline.ucsb.edu
2281:on 29 September 2014
2132:. Polarization.com.
1902:Circumhorizontal arc
1863:South Africa as the
1833:German Peasants' War
1624:, work published by
1348:
1285:night vision goggles
1250:circumhorizontal arc
795:Double rainbow with
631:
232:. Later he included
16:For other uses, see
5870:List of web colours
5865:List of RAL colours
5271:Colour reproduction
5236:LĂźscher colour test
5073:Colour of chemicals
4921:, article from the
4739:Thames & Hudson
4735:The Rainbow Goblins
4421:24 May 2016 at the
4356:1977SciAm.236d.116N
4344:Scientific American
4286:1838TCaPS...6..379A
4207:1989BAMS...70..750G
4024:Dong, Paul (2000).
3848:"Sea Water Rainbow"
3821:"Rainbows on Titan"
3719:3 June 2012 at the
3625:1998JOSAB..15.2782N
3566:1977SciAm.237a.138W
3554:Scientific American
3423:2011ApOpt..50F.129T
3334:2011ApOpt..50F.134G
3285:"Untitled Document"
3028:. Philiplaven.com.
3026:"Circular rainbows"
2858:2015ApOpt..54B.117H
2761:"Secondary rainbow"
2589:"Sea Water Rainbow"
2414:"UCSB Science Line"
2362:. 29 October 2014.
2242:Gage, John (1994).
2065:on 29 January 2015.
2059:Weather Underground
2028:National Geographic
1984:Tony Buick (2010).
1823:Army National Guard
1673:Rainbows in culture
1618:George Biddell Airy
1584:Discourse on Method
1553:, who wrote in his
1165:supernumerary bands
927:supernumerary bands
856:Full-circle rainbow
847:supernumerary bands
56:internal reflection
5279:Colour photography
5231:Colour preferences
5174:Impossible colours
5164:Colour vision test
5159:Colour temperature
5137:Colour calibration
5066:Animal colouration
4939:Atmospheric Optics
4876:Dover Publications
4326:Annalen der Physik
4292:G. B. Airy (1849)
4240:"Sir Isaac Newton"
3878:Atmospheric Optics
3852:Atmospheric Optics
3799:Atmospheric Optics
3768:www.atoptics.co.uk
3651:www.atoptics.co.uk
3307:www.atoptics.co.uk
3289:www.atoptics.co.uk
3231:. Atoptics.co.uk.
3176:"Bows everywhere!"
3132:www.atoptics.co.uk
3114:www.atoptics.co.uk
3096:www.atoptics.co.uk
3078:www.atoptics.co.uk
2765:www.atoptics.co.uk
2619:Atmospheric Optics
2593:Atmospheric Optics
2392:Atmospheric Optics
2269:Allchin, Douglas.
2184:Dover Publications
1897:Circumzenithal arc
1892:Atmospheric optics
1700:
1691:1803 depiction by
1646:
1576:
1547:Robert Grosseteste
1511:Persian astronomer
1492:Song dynasty China
1427:Seneca the Younger
1397:Scientific history
1373:
1301:
1277:Titan's hazy skies
1220:
1217:circumscribed halo
1193:
1160:
1125:
1094:light produced by
1026:
1016:Monochrome rainbow
1010:Monochrome rainbow
999:reflection rainbow
984:
918:
914:High dynamic range
880:supernumerary bows
866:
842:
805:
801:supernumerary bows
721:
603:. Therefore, from
486:
105:
48:optical phenomenon
40:
6021:
6020:
5961:
5960:
5743:
5742:
5667:Colour dimensions
5656:Human skin colour
5535:
5534:
5525:Theory of Colours
5423:Analogous colours
5367:
5366:
5301:Colour management
5218:Colour psychology
5100:Colour perception
4904:978-0-521-80925-2
4885:978-0-486-20196-2
4860:978-0-387-97935-9
4837:978-0-521-77504-5
4818:978-0-271-01977-2
4791:978-0-19-521833-6
4748:978-0-500-27759-1
4722:978-0-691-08457-2
4104:Lindberg, David C
4089:978-0-271-01977-2
4035:978-0-8351-2676-2
3933:978-0-271-01977-2
3874:"Glass Bead Bows"
3531:10.24033/asens.43
3417:(28): F129âF133.
3328:(28): F134âF141.
2883:ScienceDaily.com,
2615:"Zero order glow"
2271:"Newton's Colors"
2255:978-0-520-22611-1
2245:Color and Meaning
1873:Rainbow Coalition
1693:Joseph Anton Koch
1581:' 1637 treatise,
1419: 65 AD
1368:
991:reflected rainbow
699:
693:
684:
641:
340:
339:
129:visual perception
6066:
6049:Heraldic charges
6011:
6010:
6001:
6000:
5801:
5800:
5546:
5545:
5478:Secondary colour
5389:
5388:
5375:
5251:National colours
5246:Political colour
5226:Colour symbolism
5184:Opponent process
5142:Colour constancy
5120:Colour blindness
5051:Spectral colours
5019:
5018:
4998:
4991:
4984:
4975:
4974:
4964:
4908:
4889:
4864:
4841:
4822:
4795:
4761:
4758:The Rainbow Book
4752:
4726:
4694:
4693:
4691:
4689:
4680:. 15 June 2022.
4670:
4664:
4663:
4661:
4659:
4616:
4610:
4609:
4607:
4605:
4593:Gonzalez, Nora.
4590:
4584:
4583:
4582:
4580:
4561:
4555:
4538:
4532:
4531:
4504:
4498:
4485:
4479:
4476:
4470:
4457:
4448:
4435:
4426:
4412:
4406:
4393:
4387:
4374:
4368:
4367:
4339:
4333:
4311:
4305:
4289:
4262:
4256:
4255:
4253:
4251:
4235:
4229:
4228:
4218:
4186:
4180:
4179:
4151:
4145:
4138:
4132:
4131:
4100:
4094:
4093:
4073:
4067:
4066:
4064:
4062:
4046:
4040:
4039:
4021:
4015:
4014:
4006:
4000:
3997:
3991:
3990:
3988:
3986:
3966:
3955:
3954:
3944:
3938:
3937:
3917:
3911:
3910:
3903:classics.mit.edu
3895:
3889:
3888:
3886:
3884:
3869:
3863:
3862:
3860:
3858:
3843:
3837:
3836:
3834:
3832:
3823:. Archived from
3816:
3810:
3809:
3807:
3805:
3790:
3784:
3783:
3781:
3779:
3760:
3754:
3753:
3751:
3749:
3730:
3724:
3710:
3704:
3673:
3667:
3666:
3664:
3662:
3657:on 21 April 2008
3653:. Archived from
3643:
3637:
3636:
3608:
3602:
3599:
3590:
3589:
3587:
3585:
3545:
3536:
3535:
3533:
3509:
3503:
3502:
3487:
3481:
3480:
3465:
3459:
3458:
3406:
3400:
3399:
3397:
3395:
3376:
3370:
3369:
3317:
3311:
3310:
3299:
3293:
3292:
3281:
3275:
3274:
3272:
3270:
3251:
3245:
3244:
3242:
3240:
3225:
3219:
3218:
3216:
3214:
3193:
3187:
3186:
3184:
3182:
3171:
3165:
3142:
3136:
3135:
3124:
3118:
3117:
3106:
3100:
3099:
3088:
3082:
3081:
3070:
3064:
3063:
3048:
3042:
3041:
3039:
3037:
3021:
3015:
3014:
3012:
3010:
2995:
2989:
2988:
2986:
2984:
2969:
2963:
2962:
2960:
2958:
2952:
2929:
2911:
2902:
2896:
2877:
2852:(4): B117âB127.
2834:
2828:
2827:
2825:
2823:
2812:
2806:
2775:
2769:
2768:
2757:
2751:
2750:
2748:
2746:
2740:
2733:
2724:
2718:
2717:
2715:
2713:
2694:
2688:
2687:
2672:
2666:
2665:
2663:
2661:
2641:
2635:
2634:
2632:
2630:
2610:
2604:
2603:
2601:
2599:
2584:
2578:
2577:
2575:
2573:
2562:"About Rainbows"
2558:
2552:
2551:
2549:
2547:
2541:
2510:
2501:
2495:
2494:
2486:
2480:
2479:
2460:10.1037/h0032606
2440:
2434:
2433:
2431:
2429:
2410:
2404:
2403:
2401:
2399:
2382:
2376:
2375:
2373:
2371:
2352:
2346:
2345:
2332:
2326:
2325:
2323:
2321:
2297:
2291:
2290:
2288:
2286:
2277:. Archived from
2266:
2260:
2259:
2239:
2233:
2232:
2230:
2228:
2207:
2198:
2197:
2173:
2164:
2157:
2146:
2145:
2143:
2141:
2126:
2120:
2119:
2117:
2115:
2100:
2094:
2093:
2091:
2089:
2073:
2067:
2066:
2050:
2044:
2043:
2041:
2039:
2020:
2014:
2013:
2011:
2009:
1981:
1964:
1961:
1955:
1952:
1946:
1943:
1760:Tibetan Buddhism
1758:. Some forms of
1560:
1496:scholar-official
1420:
1417:
1388:
1382:
1380:
1379:
1376:{\displaystyle }
1374:
1369:
1361:
1343:
1329:
1323:
864:Circular rainbow
822:Alexander's band
797:Alexander's band
770:
759:
749:
739:
730:
728:
727:
722:
717:
716:
704:
700:
698:
694:
689:
686:
685:
683:
682:
664:
658:
643:
642:
639:
623:
618:, and solve for
617:
602:
596:
586:
564:
558:
547:
521:
515:
504:
497:
442:
439:Caustic (optics)
425:refractive index
408:
393:
262:
261:
102:ring-billed gull
6074:
6073:
6069:
6068:
6067:
6065:
6064:
6063:
6024:
6023:
6022:
6017:
5989:
5957:
5874:
5792:
5749:
5739:
5662:
5641:Blue in culture
5637:Colour history
5612:
5531:
5505:Colour analysis
5500:Colour triangle
5454:
5411:black-and-white
5383:
5376:
5363:
5306:Colour printing
5265:
5212:
5094:
5008:
5002:
4915:
4905:
4886:
4861:
4851:Springer-Verlag
4838:
4819:
4792:
4768:De Young Museum
4749:
4723:
4703:
4701:Further reading
4698:
4697:
4687:
4685:
4672:
4671:
4667:
4657:
4655:
4617:
4613:
4603:
4601:
4591:
4587:
4578:
4576:
4563:
4562:
4558:
4552:Wayback Machine
4539:
4535:
4528:
4520:. p. 323.
4505:
4501:
4496:Wayback Machine
4486:
4482:
4477:
4473:
4468:Wayback Machine
4458:
4451:
4446:Wayback Machine
4436:
4429:
4423:Wayback Machine
4413:
4409:
4404:Wayback Machine
4394:
4390:
4385:Wayback Machine
4375:
4371:
4340:
4336:
4322:Wayback Machine
4312:
4308:
4263:
4259:
4249:
4247:
4236:
4232:
4187:
4183:
4152:
4148:
4139:
4135:
4101:
4097:
4090:
4074:
4070:
4060:
4058:
4047:
4043:
4036:
4022:
4018:
4007:
4003:
3998:
3994:
3984:
3982:
3967:
3958:
3945:
3941:
3934:
3918:
3914:
3897:
3896:
3892:
3882:
3880:
3870:
3866:
3856:
3854:
3844:
3840:
3830:
3828:
3817:
3813:
3803:
3801:
3791:
3787:
3777:
3775:
3762:
3761:
3757:
3747:
3745:
3732:
3731:
3727:
3721:Wayback Machine
3711:
3707:
3701:(181): 453â461.
3686:Wayback Machine
3674:
3670:
3660:
3658:
3645:
3644:
3640:
3609:
3605:
3600:
3593:
3583:
3581:
3546:
3539:
3510:
3506:
3489:
3488:
3484:
3467:
3466:
3462:
3407:
3403:
3393:
3391:
3378:
3377:
3373:
3318:
3314:
3301:
3300:
3296:
3283:
3282:
3278:
3268:
3266:
3253:
3252:
3248:
3238:
3236:
3227:
3226:
3222:
3212:
3210:
3194:
3190:
3180:
3178:
3172:
3168:
3143:
3139:
3126:
3125:
3121:
3108:
3107:
3103:
3090:
3089:
3085:
3072:
3071:
3067:
3050:
3049:
3045:
3035:
3033:
3022:
3018:
3008:
3006:
2997:
2996:
2992:
2982:
2980:
2971:
2970:
2966:
2956:
2954:
2950:
2927:10.1.1.296.3051
2909:
2903:
2899:
2892:Wayback Machine
2885:August 6, 2012.
2835:
2831:
2821:
2819:
2814:
2813:
2809:
2776:
2772:
2759:
2758:
2754:
2744:
2742:
2738:
2731:
2725:
2721:
2711:
2709:
2696:
2695:
2691:
2674:
2673:
2669:
2659:
2657:
2642:
2638:
2628:
2626:
2611:
2607:
2597:
2595:
2585:
2581:
2571:
2569:
2564:. Eo.ucar.edu.
2560:
2559:
2555:
2545:
2543:
2539:
2508:
2502:
2498:
2487:
2483:
2441:
2437:
2427:
2425:
2412:
2411:
2407:
2397:
2395:
2383:
2379:
2369:
2367:
2354:
2353:
2349:
2333:
2329:
2319:
2317:
2298:
2294:
2284:
2282:
2267:
2263:
2256:
2240:
2236:
2226:
2224:
2209:
2208:
2201:
2194:
2186:. p. 193.
2174:
2167:
2158:
2149:
2139:
2137:
2128:
2127:
2123:
2113:
2111:
2102:
2101:
2097:
2087:
2085:
2074:
2070:
2051:
2047:
2037:
2035:
2022:
2021:
2017:
2007:
2005:
1998:
1982:
1978:
1973:
1968:
1967:
1962:
1958:
1953:
1949:
1944:
1940:
1935:
1888:
1776:Greek mythology
1738:in present-day
1716:Norse mythology
1708:Book of Genesis
1697:Book of Genesis
1685:
1679:
1671:Main articles:
1669:
1638:
1545:and studied by
1418:
1399:
1393:and vanishing.
1391:antisolar point
1384:
1360:
1349:
1346:
1345:
1339:
1336:incidence angle
1334:, the critical
1325:
1318:
1293:
1265:
1259:
1209:
1185:
1157:Brocken spectre
1149:
1143:
1114:
1108:
1042:
1018:
1012:
974:
931:stacker rainbow
907:
858:
834:
832:Twinned rainbow
789:
782:
780:Double rainbows
777:
765:
754:
748:
741:
735:
712:
708:
688:
687:
678:
674:
663:
659:
657:
653:
638:
634:
632:
629:
628:
624:, which yields
619:
608:
598:
592:
569:
560:
553:
530:
517:
506:
499:
492:
478:
416:
415:
414:
413:
412:
409:
400:
399:
398:
394:
383:
192:
186:
144:wide-angle lens
94:
36:antisolar point
26:
21:
12:
11:
5:
6072:
6062:
6061:
6056:
6051:
6046:
6041:
6036:
6019:
6018:
6016:
6015:
6005:
5994:
5991:
5990:
5988:
5987:
5982:
5977:
5971:
5969:
5963:
5962:
5959:
5958:
5956:
5955:
5950:
5945:
5940:
5935:
5930:
5925:
5920:
5915:
5910:
5905:
5900:
5895:
5890:
5884:
5882:
5876:
5875:
5873:
5872:
5867:
5862:
5857:
5856:
5855:
5845:
5840:
5835:
5830:
5825:
5820:
5815:
5809:
5807:
5798:
5794:
5793:
5791:
5790:
5785:
5780:
5774:
5769:
5764:
5759:
5753:
5751:
5745:
5744:
5741:
5740:
5738:
5737:
5732:
5727:
5726:
5725:
5720:
5715:
5710:
5705:
5695:
5694:
5693:
5691:Pastel colours
5683:
5682:
5681:
5670:
5668:
5664:
5663:
5661:
5660:
5659:
5658:
5653:
5648:
5643:
5635:
5634:
5633:
5622:
5620:
5614:
5613:
5611:
5610:
5605:
5600:
5595:
5590:
5585:
5580:
5575:
5570:
5565:
5560:
5554:
5552:
5543:
5537:
5536:
5533:
5532:
5530:
5529:
5521:
5520:(Schopenhauer)
5513:
5508:
5502:
5497:
5492:
5487:
5482:
5481:
5480:
5475:
5473:Primary colour
5464:
5462:
5456:
5455:
5453:
5452:
5447:
5442:
5437:
5436:
5435:
5430:
5425:
5420:
5415:
5414:
5413:
5397:
5395:
5386:
5378:
5377:
5370:
5368:
5365:
5364:
5362:
5361:
5359:Colour mapping
5356:
5351:
5350:
5349:
5348:
5347:
5337:
5336:
5335:
5320:
5319:
5318:
5313:
5303:
5298:
5293:
5292:
5291:
5286:
5284:Colour balance
5275:
5273:
5267:
5266:
5264:
5263:
5258:
5253:
5248:
5243:
5241:Kruithof curve
5238:
5233:
5228:
5222:
5220:
5214:
5213:
5211:
5210:
5203:
5198:
5197:
5196:
5191:
5181:
5176:
5171:
5166:
5161:
5156:
5155:
5154:
5144:
5139:
5134:
5133:
5132:
5127:
5117:
5116:
5115:
5113:Sonochromatism
5104:
5102:
5096:
5095:
5093:
5092:
5087:
5082:
5081:
5080:
5070:
5069:
5068:
5063:
5053:
5048:
5047:
5046:
5041:
5036:
5025:
5023:
5022:Colour physics
5016:
5014:Colour science
5010:
5009:
5001:
5000:
4993:
4986:
4978:
4972:
4971:
4965:
4944:
4935:
4930:
4925:
4914:
4913:External links
4911:
4910:
4909:
4903:
4890:
4884:
4865:
4859:
4842:
4836:
4823:
4817:
4796:
4790:
4771:
4753:
4747:
4727:
4721:
4702:
4699:
4696:
4695:
4665:
4611:
4585:
4556:
4533:
4526:
4499:
4480:
4471:
4449:
4427:
4407:
4388:
4369:
4334:
4328:, 4th series,
4313:G. Mie (1908)
4306:
4304:
4303:
4290:
4280:(3): 379â403.
4257:
4230:
4201:(7): 750â751.
4181:
4168:10.1086/349399
4146:
4133:
4120:10.1086/350116
4095:
4088:
4068:
4041:
4034:
4016:
4001:
3992:
3956:
3939:
3932:
3912:
3890:
3864:
3838:
3819:Science@NASA.
3811:
3785:
3755:
3725:
3705:
3703:
3702:
3688:
3668:
3638:
3603:
3591:
3537:
3504:
3482:
3460:
3411:Applied Optics
3401:
3371:
3322:Applied Optics
3312:
3294:
3276:
3259:atoptics.co.uk
3246:
3220:
3188:
3166:
3164:
3163:
3158:
3137:
3119:
3101:
3083:
3065:
3043:
3016:
2990:
2964:
2897:
2895:
2894:
2878:
2846:Applied Optics
2829:
2807:
2805:
2804:
2793:
2790:On Aristotle's
2770:
2752:
2719:
2689:
2667:
2636:
2605:
2579:
2553:
2519:(3): 369â398.
2496:
2481:
2435:
2405:
2377:
2347:
2327:
2292:
2261:
2254:
2234:
2199:
2193:978-0486421186
2192:
2165:
2159:Isaac Newton,
2147:
2121:
2110:on 28 May 2013
2095:
2084:on 25 May 2007
2068:
2045:
2015:
1996:
1975:
1974:
1972:
1969:
1966:
1965:
1956:
1947:
1937:
1936:
1934:
1931:
1930:
1929:
1924:
1919:
1914:
1909:
1904:
1899:
1894:
1887:
1884:
1869:Apple computer
1865:rainbow nation
1857:Nelson Mandela
1855:and President
1778:, the goddess
1744:BogotĂĄ savanna
1668:
1665:
1654:Florence flask
1637:
1634:
1622:Mie scattering
1539:Book of Optics
1484:Book of Optics
1455:Ibn al-Haytham
1448:Arab physicist
1437:concave mirror
1398:
1395:
1372:
1367:
1364:
1359:
1356:
1353:
1332:natural number
1322: + 1
1292:
1289:
1261:Main article:
1258:
1255:
1224:circumzenithal
1208:
1205:
1184:
1181:
1145:Main article:
1142:
1139:
1110:Main article:
1107:
1104:
1041:
1038:
1014:Main article:
1011:
1008:
973:
970:
906:
903:
857:
854:
833:
830:
809:double rainbow
786:Double Rainbow
781:
778:
776:
773:
746:
732:
731:
720:
715:
711:
707:
703:
697:
692:
681:
677:
673:
670:
667:
662:
656:
652:
649:
646:
637:
589:
588:
550:
549:
477:
474:
464:axial symmetry
410:
403:
402:
401:
395:
388:
387:
386:
385:
384:
382:
379:
338:
337:
334:
331:
328:
325:
322:
319:
316:
312:
311:
308:
305:
302:
299:
296:
293:
290:
286:
285:
282:
280:
277:
274:
271:
269:
266:
190:Spectral color
185:
182:
138:of 84°. For a
113:altitude angle
93:
90:
24:
9:
6:
4:
3:
2:
6071:
6060:
6057:
6055:
6054:LGBTQ symbols
6052:
6050:
6047:
6045:
6044:Lucky symbols
6042:
6040:
6037:
6035:
6032:
6031:
6029:
6014:
6006:
6004:
5996:
5995:
5992:
5986:
5983:
5981:
5978:
5976:
5973:
5972:
5970:
5968:
5964:
5954:
5951:
5949:
5946:
5944:
5941:
5939:
5936:
5934:
5931:
5929:
5926:
5924:
5921:
5919:
5916:
5914:
5911:
5909:
5906:
5904:
5901:
5899:
5896:
5894:
5891:
5889:
5886:
5885:
5883:
5881:
5877:
5871:
5868:
5866:
5863:
5861:
5858:
5854:
5851:
5850:
5849:
5846:
5844:
5841:
5839:
5836:
5834:
5831:
5829:
5826:
5824:
5821:
5819:
5816:
5814:
5811:
5810:
5808:
5806:
5802:
5799:
5795:
5789:
5786:
5784:
5781:
5778:
5775:
5773:
5770:
5768:
5765:
5763:
5760:
5758:
5755:
5754:
5752:
5750:organisations
5746:
5736:
5733:
5731:
5728:
5724:
5721:
5719:
5716:
5714:
5711:
5709:
5706:
5704:
5701:
5700:
5699:
5696:
5692:
5689:
5688:
5687:
5686:Colourfulness
5684:
5680:
5677:
5676:
5675:
5672:
5671:
5669:
5665:
5657:
5654:
5652:
5649:
5647:
5644:
5642:
5639:
5638:
5636:
5632:
5629:
5628:
5627:
5624:
5623:
5621:
5619:
5615:
5609:
5606:
5604:
5601:
5599:
5596:
5594:
5591:
5589:
5586:
5584:
5581:
5579:
5576:
5574:
5571:
5569:
5566:
5564:
5561:
5559:
5556:
5555:
5553:
5551:
5547:
5544:
5542:
5538:
5527:
5526:
5522:
5519:
5518:
5514:
5512:
5509:
5506:
5503:
5501:
5498:
5496:
5493:
5491:
5488:
5486:
5483:
5479:
5476:
5474:
5471:
5470:
5469:
5468:Colour mixing
5466:
5465:
5463:
5461:
5460:Colour theory
5457:
5451:
5448:
5446:
5443:
5441:
5440:Light-on-dark
5438:
5434:
5431:
5429:
5426:
5424:
5421:
5419:
5416:
5412:
5409:
5408:
5407:
5404:
5403:
5402:
5399:
5398:
5396:
5394:
5393:Colour scheme
5390:
5387:
5385:
5379:
5374:
5360:
5357:
5355:
5352:
5346:
5343:
5342:
5341:
5338:
5334:
5331:
5330:
5329:
5326:
5325:
5324:
5321:
5317:
5314:
5312:
5309:
5308:
5307:
5304:
5302:
5299:
5297:
5294:
5290:
5287:
5285:
5282:
5281:
5280:
5277:
5276:
5274:
5272:
5268:
5262:
5261:Chromotherapy
5259:
5257:
5254:
5252:
5249:
5247:
5244:
5242:
5239:
5237:
5234:
5232:
5229:
5227:
5224:
5223:
5221:
5219:
5215:
5209:
5208:
5204:
5202:
5201:Tetrachromacy
5199:
5195:
5192:
5190:
5187:
5186:
5185:
5182:
5180:
5177:
5175:
5172:
5170:
5167:
5165:
5162:
5160:
5157:
5153:
5150:
5149:
5148:
5145:
5143:
5140:
5138:
5135:
5131:
5128:
5126:
5125:Achromatopsia
5123:
5122:
5121:
5118:
5114:
5111:
5110:
5109:
5108:Chromesthesia
5106:
5105:
5103:
5101:
5097:
5091:
5088:
5086:
5083:
5079:
5076:
5075:
5074:
5071:
5067:
5064:
5062:
5059:
5058:
5057:
5054:
5052:
5049:
5045:
5042:
5040:
5037:
5035:
5032:
5031:
5030:
5027:
5026:
5024:
5020:
5017:
5015:
5011:
5006:
4999:
4994:
4992:
4987:
4985:
4980:
4979:
4976:
4969:
4966:
4962:
4958:
4954:
4953:Sixty Symbols
4950:
4945:
4942:
4940:
4936:
4934:
4931:
4929:
4926:
4924:
4920:
4917:
4916:
4906:
4900:
4896:
4891:
4887:
4881:
4877:
4873:
4872:
4866:
4862:
4856:
4852:
4848:
4843:
4839:
4833:
4829:
4824:
4820:
4814:
4810:
4806:
4802:
4797:
4793:
4787:
4783:
4779:
4778:
4772:
4769:
4765:
4759:
4754:
4750:
4744:
4740:
4736:
4732:
4728:
4724:
4718:
4714:
4710:
4705:
4704:
4683:
4679:
4675:
4669:
4653:
4649:
4645:
4641:
4637:
4633:
4629:
4625:
4622:(June 2021).
4621:
4620:Blust, Robert
4615:
4600:
4596:
4589:
4574:
4570:
4569:mistholme.com
4566:
4560:
4553:
4549:
4546:
4542:
4537:
4529:
4527:9781570627729
4523:
4519:
4515:
4514:
4509:
4508:Ray, Reginald
4503:
4497:
4493:
4490:
4484:
4475:
4469:
4465:
4462:
4456:
4454:
4447:
4443:
4440:
4434:
4432:
4424:
4420:
4417:
4411:
4405:
4401:
4398:
4392:
4386:
4382:
4379:
4373:
4365:
4361:
4357:
4353:
4349:
4345:
4338:
4332:(3): 377â445.
4331:
4327:
4323:
4319:
4316:
4310:
4301:
4298:
4295:
4291:
4287:
4283:
4279:
4275:
4271:
4266:
4265:
4261:
4245:
4241:
4234:
4226:
4222:
4217:
4212:
4208:
4204:
4200:
4196:
4192:
4185:
4177:
4173:
4169:
4165:
4161:
4157:
4150:
4143:
4137:
4129:
4125:
4121:
4117:
4113:
4109:
4105:
4099:
4091:
4085:
4081:
4080:
4072:
4056:
4052:
4045:
4037:
4031:
4027:
4020:
4012:
4005:
3996:
3980:
3976:
3972:
3965:
3963:
3961:
3952:
3951:
3943:
3935:
3929:
3925:
3924:
3916:
3908:
3904:
3900:
3894:
3879:
3875:
3872:Cowley, Les.
3868:
3853:
3849:
3846:Cowley, Les.
3842:
3826:
3822:
3815:
3800:
3796:
3793:Cowley, Les.
3789:
3773:
3769:
3765:
3759:
3743:
3739:
3735:
3729:
3722:
3718:
3715:
3709:
3700:
3696:
3693:
3689:
3687:
3683:
3680:
3677:
3676:
3672:
3656:
3652:
3648:
3642:
3634:
3630:
3626:
3622:
3618:
3614:
3607:
3598:
3596:
3579:
3575:
3571:
3567:
3563:
3559:
3555:
3551:
3544:
3542:
3532:
3527:
3524:(5): 67â109.
3523:
3519:
3515:
3508:
3500:
3496:
3492:
3486:
3478:
3474:
3470:
3464:
3456:
3452:
3448:
3444:
3440:
3436:
3432:
3428:
3424:
3420:
3416:
3412:
3405:
3389:
3385:
3383:
3375:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3327:
3323:
3316:
3308:
3304:
3298:
3290:
3286:
3280:
3264:
3260:
3256:
3250:
3234:
3230:
3224:
3209:
3205:
3204:
3199:
3192:
3177:
3170:
3162:
3159:
3156:
3153:
3150:
3146:
3145:
3141:
3133:
3129:
3123:
3115:
3111:
3105:
3097:
3093:
3087:
3079:
3075:
3069:
3061:
3057:
3056:apod.nasa.gov
3053:
3047:
3031:
3027:
3020:
3004:
3000:
2994:
2978:
2974:
2968:
2949:
2945:
2941:
2937:
2933:
2928:
2923:
2919:
2915:
2908:
2901:
2893:
2889:
2886:
2884:
2879:
2875:
2871:
2867:
2863:
2859:
2855:
2851:
2847:
2843:
2838:
2837:
2833:
2817:
2811:
2802:
2798:
2794:
2791:
2787:
2783:
2779:
2778:
2774:
2766:
2762:
2756:
2737:
2730:
2723:
2707:
2703:
2699:
2693:
2685:
2681:
2677:
2671:
2655:
2651:
2647:
2640:
2624:
2620:
2616:
2613:Cowley, Les.
2609:
2594:
2590:
2587:Cowley, Les.
2583:
2567:
2563:
2557:
2538:
2534:
2530:
2526:
2522:
2518:
2514:
2507:
2500:
2492:
2485:
2477:
2473:
2469:
2465:
2461:
2457:
2453:
2449:
2445:
2439:
2423:
2419:
2415:
2409:
2394:
2393:
2388:
2385:Cowley, Les.
2381:
2365:
2361:
2357:
2351:
2343:
2342:
2337:
2336:Newton, Isaac
2331:
2315:
2311:
2307:
2305:
2296:
2280:
2276:
2272:
2265:
2257:
2251:
2247:
2246:
2238:
2222:
2218:
2217:
2212:
2206:
2204:
2195:
2189:
2185:
2181:
2180:
2172:
2170:
2162:
2156:
2154:
2152:
2135:
2131:
2125:
2109:
2105:
2099:
2083:
2079:
2072:
2064:
2060:
2056:
2049:
2033:
2029:
2025:
2019:
2003:
1999:
1997:9781441910530
1993:
1989:
1988:
1980:
1976:
1960:
1951:
1942:
1938:
1928:
1925:
1923:
1920:
1918:
1915:
1913:
1910:
1908:
1905:
1903:
1900:
1898:
1895:
1893:
1890:
1889:
1883:
1879:
1876:
1874:
1870:
1866:
1862:
1858:
1854:
1850:
1849:Gilbert Baker
1846:
1842:
1838:
1834:
1830:
1829:Rainbow flags
1826:
1824:
1820:
1816:
1812:
1808:
1804:
1800:
1796:
1792:
1788:
1783:
1781:
1777:
1773:
1769:
1765:
1761:
1757:
1753:
1749:
1745:
1741:
1737:
1733:
1729:
1725:
1721:
1717:
1713:
1709:
1705:
1698:
1694:
1689:
1684:
1678:
1674:
1664:
1661:
1657:
1655:
1651:
1642:
1633:
1631:
1627:
1623:
1619:
1614:
1613:with itself.
1612:
1608:
1603:
1598:
1596:
1592:
1587:
1585:
1580:
1572:
1568:
1565:
1559:
1558:
1552:
1548:
1544:
1540:
1535:
1532:
1528:
1524:
1520:
1516:
1512:
1507:
1505:
1501:
1497:
1493:
1488:
1486:
1485:
1480:
1476:
1472:
1468:
1464:
1460:
1456:
1453:
1449:
1444:
1442:
1438:
1433:
1428:
1424:
1413:
1412:
1408:In Book I of
1406:
1404:
1394:
1392:
1387:
1365:
1362:
1357:
1354:
1342:
1337:
1333:
1328:
1321:
1316:
1310:
1307:
1297:
1288:
1287:to see them.
1286:
1282:
1278:
1274:
1270:
1264:
1254:
1251:
1246:
1244:
1239:
1237:
1233:
1229:
1225:
1218:
1213:
1204:
1202:
1198:
1189:
1180:
1178:
1173:
1171:
1166:
1158:
1153:
1148:
1138:
1136:
1135:
1130:
1129:lunar rainbow
1123:
1122:Yosemite Fall
1118:
1113:
1103:
1099:
1097:
1093:
1089:
1085:
1079:
1077:
1073:
1069:
1065:
1060:
1056:
1052:
1048:
1037:
1036:
1032:
1022:
1017:
1007:
1003:
1000:
995:
992:
987:
980:
976:
969:
967:
963:
959:
955:
951:
947:
943:
938:
936:
932:
928:
924:
915:
911:
902:
900:
896:
892:
888:
883:
881:
877:
876:secondary bow
872:
862:
853:
850:
848:
838:
829:
827:
823:
817:
813:
810:
802:
798:
793:
787:
772:
768:
763:
757:
751:
745:
738:
718:
713:
709:
705:
701:
695:
690:
679:
675:
671:
668:
665:
660:
654:
650:
647:
644:
635:
627:
626:
625:
622:
615:
611:
607:, we can set
606:
601:
595:
584:
580:
576:
572:
568:
567:
566:
563:
556:
546:
542:
538:
534:
529:
528:
527:
525:
520:
514:
510:
503:
496:
489:
482:
473:
470:
465:
459:
457:
452:
450:
446:
440:
434:
428:
426:
421:
407:
392:
378:
376:
372:
367:
365:
361:
357:
352:
350:
346:
335:
332:
329:
326:
323:
320:
317:
314:
313:
309:
306:
303:
300:
297:
294:
291:
288:
287:
283:
281:
278:
275:
272:
270:
267:
264:
263:
260:
258:
254:
250:
246:
243:
242:ancient Greek
239:
235:
231:
227:
223:
219:
215:
210:
208:
204:
201:
197:
191:
181:
179:
174:
170:
168:
164:
159:
157:
153:
149:
145:
141:
137:
136:angle of view
132:
130:
126:
121:
118:
114:
110:
103:
98:
89:
85:
83:
78:
75:
73:
69:
65:
61:
57:
53:
49:
45:
37:
32:
28:
23:
19:
5860:Colour chart
5723:Fluorescence
5679:Dichromatism
5541:Colour terms
5523:
5515:
5495:Colour wheel
5490:Colour solid
5485:Chromaticity
5354:Colour space
5323:Colour model
5256:Chromophobia
5205:
5038:
4952:
4938:
4894:
4870:
4846:
4827:
4803:. New York:
4800:
4776:
4763:
4757:
4734:
4708:
4686:. Retrieved
4677:
4668:
4656:. Retrieved
4631:
4627:
4614:
4602:. Retrieved
4598:
4588:
4577:, retrieved
4568:
4559:
4536:
4512:
4502:
4483:
4474:
4410:
4391:
4372:
4347:
4343:
4337:
4329:
4325:
4309:
4299:
4296:
4277:
4273:
4260:
4248:. Retrieved
4233:
4198:
4194:
4184:
4162:(2): 95â98.
4159:
4155:
4149:
4141:
4136:
4111:
4107:
4098:
4078:
4071:
4059:. Retrieved
4044:
4025:
4019:
4010:
4004:
3995:
3983:. Retrieved
3949:
3942:
3922:
3915:
3902:
3893:
3881:. Retrieved
3877:
3867:
3855:. Retrieved
3851:
3841:
3829:. Retrieved
3825:the original
3814:
3802:. Retrieved
3798:
3788:
3776:. Retrieved
3767:
3758:
3746:. Retrieved
3738:johncohn.org
3737:
3728:
3712:Les Cowley.
3708:
3698:
3697:, series 5,
3694:
3671:
3659:. Retrieved
3655:the original
3650:
3641:
3619:(11): 2782.
3616:
3612:
3606:
3582:. Retrieved
3557:
3553:
3521:
3517:
3507:
3494:
3485:
3472:
3463:
3414:
3410:
3404:
3392:. Retrieved
3381:
3374:
3325:
3321:
3315:
3306:
3297:
3288:
3279:
3267:. Retrieved
3258:
3249:
3237:. Retrieved
3223:
3211:. Retrieved
3201:
3191:
3179:. Retrieved
3169:
3154:
3151:
3140:
3131:
3122:
3113:
3104:
3095:
3086:
3077:
3068:
3055:
3046:
3034:. Retrieved
3019:
3007:. Retrieved
2993:
2981:. Retrieved
2967:
2955:. Retrieved
2917:
2913:
2900:
2882:
2849:
2845:
2832:
2820:. Retrieved
2810:
2796:
2789:
2785:
2781:
2773:
2764:
2755:
2743:. Retrieved
2722:
2710:. Retrieved
2701:
2692:
2680:earthsky.org
2679:
2670:
2658:. Retrieved
2649:
2639:
2627:. Retrieved
2618:
2608:
2596:. Retrieved
2592:
2582:
2570:. Retrieved
2556:
2544:. Retrieved
2516:
2512:
2499:
2490:
2484:
2454:(1): 10â20.
2451:
2447:
2438:
2426:. Retrieved
2417:
2408:
2396:. Retrieved
2390:
2380:
2368:. Retrieved
2360:ScienceAlert
2359:
2350:
2340:
2330:
2318:. Retrieved
2310:Colour Music
2309:
2303:
2295:
2283:. Retrieved
2279:the original
2274:
2264:
2244:
2237:
2225:. Retrieved
2214:
2178:
2160:
2138:. Retrieved
2124:
2112:. Retrieved
2108:the original
2098:
2086:. Retrieved
2082:the original
2071:
2063:the original
2058:
2048:
2036:. Retrieved
2027:
2018:
2006:. Retrieved
1986:
1979:
1959:
1950:
1941:
1880:
1877:
1853:Desmond Tutu
1827:
1784:
1770:. The Irish
1768:rainbow body
1766:reference a
1704:in mythology
1701:
1683:Rainbow flag
1662:
1658:
1647:
1615:
1607:Thomas Young
1599:
1582:
1577:
1538:
1536:
1526:
1522:
1508:
1489:
1482:
1467:experimental
1462:
1458:
1445:
1425:philosopher
1409:
1407:
1400:
1385:
1340:
1326:
1319:
1311:
1302:
1266:
1247:
1240:
1232:ice crystals
1221:
1194:
1174:
1161:
1132:
1128:
1126:
1100:
1087:
1083:
1080:
1075:
1072:fourth-order
1071:
1067:
1063:
1058:
1055:second-order
1054:
1050:
1046:
1043:
1035:red rainbow.
1034:
1030:
1027:
1004:
998:
996:
990:
988:
985:
975:
966:Thomas Young
946:interference
939:
930:
926:
922:
919:
899:ice crystals
884:
870:
867:
851:
843:
818:
814:
808:
806:
766:
755:
752:
743:
736:
733:
620:
613:
609:
599:
593:
590:
582:
578:
574:
570:
561:
554:
551:
544:
540:
536:
532:
518:
512:
508:
501:
494:
490:
487:
460:
453:
429:
417:
368:
353:
348:
344:
341:
249:Solar System
211:
202:
196:Isaac Newton
193:
175:
171:
160:
148:focal length
133:
122:
106:
86:
79:
76:
43:
41:
27:
22:
5718:Iridescence
5550:Basic terms
5445:Web colours
5401:Colour tool
5340:subtractive
5289:Colour cast
5194:Unique hues
5152:Colour code
5147:Colour task
5090:Colorimetry
5056:Chromophore
4957:Brady Haran
4731:De Rico, Ul
4688:7 September
4658:29 November
4634:: 145â161.
3883:10 November
3857:10 November
3831:25 November
3748:10 February
2801:pp. 110â111
2650:Ask the van
1636:Experiments
1630:Nussenzveig
1551:Roger Bacon
1084:fifth-order
1064:third-order
1047:first-order
524:Snell's law
381:Explanation
360:ultraviolet
6028:Categories
5880:Shades of:
5713:Brightness
5384:philosophy
5189:Afterimage
5179:Metamerism
5130:Dichromacy
4949:"Rainbows"
4809:SPIE Press
4579:21 October
4350:(4): 116.
4302:: 595â600.
4114:(2): 235.
3269:4 February
2712:30 October
2320:20 October
2285:16 October
1971:References
1837:LGBT pride
1815:BouffĂŠmont
1772:leprechaun
1754:and small
1681:See also:
1626:Gustav Mie
1591:refraction
1557:Opus Majus
1306:reflectors
1201:monochrome
1092:collimated
1076:quaternary
1031:monochrome
775:Variations
449:dispersion
445:wavelength
207:Roy G. Biv
188:See also:
142:camera, a
140:35 mm
92:Visibility
60:dispersion
52:refraction
50:caused by
5730:Grayscale
5703:Lightness
5698:Luminance
5507:(fashion)
5207:The dress
4648:236605041
4628:Anthropos
4565:"Rainbow"
4545:s.v. Iris
4225:1520-0477
4176:145493641
4128:170749000
4061:10 August
3439:1559-128X
3394:19 August
3350:1559-128X
3239:19 August
3036:4 October
3009:4 October
2922:CiteSeerX
2822:19 August
2572:19 August
2468:0022-1015
2398:27 August
2370:16 August
2227:16 August
2140:19 August
2114:19 August
2024:"Rainbow"
1861:apartheid
1732:Cuchavira
1611:interfere
1579:Descartes
1403:Aristotle
1363:π
1177:ice halos
1059:secondary
968:in 1804.
760:based on
714:∘
706:≈
666:−
651:
636:β
577:â arcsin(
565:, we get
526:gives us
433:luminance
420:refracted
178:polarised
152:stitching
82:refracted
6003:Category
5985:Lighting
5708:Darkness
5528:(Goethe)
5328:additive
5316:Quattron
4959:for the
4733:(1978).
4682:Archived
4678:BBC News
4652:Archived
4573:archived
4548:Archived
4510:(2001).
4492:Archived
4464:Archived
4442:Archived
4419:Archived
4400:Archived
4381:Archived
4318:Archived
4244:Archived
4055:Archived
3979:Archived
3907:Archived
3804:22 April
3772:Archived
3742:Archived
3717:Archived
3682:Archived
3584:8 August
3578:Archived
3499:Archived
3477:Archived
3455:20238055
3447:22016236
3388:Archived
3358:22016237
3263:Archived
3233:Archived
3181:13 April
3060:Archived
3030:Archived
3003:Archived
2983:12 March
2977:Archived
2948:Archived
2920:: 1â12.
2888:Archived
2874:25967817
2736:Archived
2706:Archived
2684:Archived
2660:13 April
2654:Archived
2629:8 August
2623:Archived
2566:Archived
2537:Archived
2533:11006906
2422:Archived
2364:Archived
2338:(1704).
2314:Archived
2221:Archived
2219:. 2014.
2134:Archived
2032:Archived
2002:Archived
1886:See also
1787:heraldry
1764:Dzogchen
1756:emeralds
1740:Colombia
1531:aperture
1500:Shen Kuo
1471:Averroes
1452:polymath
1441:parhelia
1324:, where
1281:infrared
1271:'s moon
1183:Sleetbow
1068:tertiary
895:22° halo
824:, after
605:calculus
371:question
356:infrared
349:spectrum
245:sophists
200:mnemonic
156:panorama
109:sunlight
64:spectrum
6034:Rainbow
5967:Related
5928:Magenta
5853:history
5757:Pantone
5044:Visible
5039:Rainbow
4352:Bibcode
4282:Bibcode
4250:19 June
4203:Bibcode
3778:2 March
3661:28 June
3621:Bibcode
3562:Bibcode
3419:Bibcode
3330:Bibcode
2944:6774839
2854:Bibcode
2745:13 June
2546:11 July
2476:5013326
2341:Opticks
2304:Opticks
1927:Moonbow
1922:Fog bow
1917:Sun dog
1811:Pfreimd
1724:Midgard
1720:BifrĂśst
1421:), the
1315:diamond
1147:Fog bow
1134:moonbow
1112:Moonbow
1088:quinary
1051:primary
935:fogbows
891:fog bow
769:= 1.343
758:= 1.330
740:yields
557:= 1.333
345:rainbow
336:Violet
324:Yellow
321:Orange
310:Violet
307:Indigo
298:Yellow
295:Orange
284:Violet
273:Yellow
146:with a
125:moonbow
44:rainbow
5980:Qualia
5975:Vision
5923:Purple
5918:Violet
5898:Yellow
5893:Orange
5748:Colour
5588:Orange
5583:Purple
5573:Yellow
5382:Colour
5007:topics
5005:Colour
4901:
4882:
4857:
4834:
4815:
4788:
4745:
4719:
4646:
4604:20 May
4524:
4223:
4174:
4126:
4086:
4032:
3985:7 June
3930:
3453:
3445:
3437:
3366:796963
3364:
3356:
3348:
3213:7 June
2942:
2924:
2872:
2598:7 June
2531:
2474:
2466:
2428:1 June
2252:
2190:
2088:7 June
2038:20 May
2008:28 May
1994:
1843:; the
1801:, and
1791:argent
1752:snails
1736:Muisca
1728:Asgard
1498:named
1432:fuller
1269:Saturn
1243:zenith
1141:Fogbow
1096:lasers
1070:) and
942:optics
648:arccos
552:where
364:opaque
327:Green
301:Green
276:Green
238:indigo
234:orange
230:violet
218:yellow
117:clouds
46:is an
6013:Index
5953:Black
5943:White
5938:Brown
5903:Green
5805:Lists
5797:Names
5779:(CIE)
5608:Brown
5603:White
5593:Black
5563:Green
5078:Water
5034:Light
4644:S2CID
4541:Smith
4264:See:
4172:S2CID
4124:S2CID
3675:See:
3451:S2CID
3362:S2CID
3144:See:
2957:9 May
2951:(PDF)
2940:S2CID
2910:(PDF)
2836:See:
2777:See:
2739:(PDF)
2732:(PDF)
2540:(PDF)
2509:(PDF)
1933:Notes
1807:Regen
1795:gules
1602:prism
1595:Snell
1423:Roman
1330:is a
1273:Titan
1236:halos
1197:sleet
1170:glory
950:phase
887:glory
871:below
531:sin(2
437:(see
333:Blue
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