HOME

TheInfoList



OR:

A rainbow is a
meteorological Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
phenomenon that is caused by reflection,
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
and
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
of light in water droplets resulting in a
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
of light appearing in the sky. It takes the form of a multicoloured circular
arc ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services * ...
. Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground, and centered on a line from the Sun to the observer's eye. In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it. In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, with red on the inner side of the arc. This is caused by the light being reflected twice on the inside of the droplet before leaving it.


Overview

A rainbow is not located at a specific distance from the observer, but comes from an optical illusion caused by any water droplets viewed from a certain angle relative to a light source. Thus, a rainbow is not an object and cannot be physically approached. Indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems "under" or "at the end of" a rainbow, the second observer will see a different rainbow—farther off—at the same angle as seen by the first observer. Rainbows span a continuous spectrum of colours. Any distinct bands perceived are an artefact of human
colour vision Color vision, a feature of visual perception, is an ability to perceive differences between light composed of different wavelengths (i.e., different spectral power distributions) independently of light intensity. Color perception is a part of t ...
, and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side. For colours seen by the human eye, the most commonly cited and remembered sequence is
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
's sevenfold red, orange, yellow, green, blue, indigo and violet, remembered by the
mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imag ...
''Richard Of York Gave Battle In Vain,'' or as the name of a fictional person (
Roy G. Biv ROYGBIV is an acronym for the sequence of hues commonly described as making up a rainbow: red, orange, yellow, green, blue, indigo, and violet. There are several mnemonics that can be used for remembering this color sequence, such as the ...
). 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. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne
dew Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening due to condensation. As the exposed surface cools by radiating its heat, atmospheric moisture condenses at a rate greater than that at whi ...
.


Visibility

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle. Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening. The most spectacular rainbow displays happen when half the sky is still dark with raining
cloud In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may co ...
s and the observer is at a spot with clear sky in the direction of the Sun. The result is a luminous rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible. It appears about 10° outside of the primary rainbow, with inverse order of colours. The rainbow effect is also commonly seen near waterfalls or fountains. In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human
visual perception Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum reflecte ...
for colour is poor in low light, moonbows are often perceived to be white. It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an
angle of view The angle of view is the decisive variable for the visual perception of the size or projection of the size of an object. Angle of view and perception of size The perceived size of an object depends on the size of the image projected onto the ...
of 84°. For a 35 mm camera, a
wide-angle lens In photography and cinematography, a wide-angle lens refers to a lens whose focal length is substantially smaller than the focal length of a normal lens for a given film plane. This type of lens allows more of the scene to be included in the pho ...
with a
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
of 19 mm or less would be required. Now that software for stitching several images into a
panorama A panorama (formed from Greek πᾶν "all" + ὅραμα "view") is any wide-angle view or representation of a physical space, whether in painting, drawing, photography, film, seismic images, or 3D modeling. The word was originally coined in ...
is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames. From above the Earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle. This phenomenon can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°. The sky inside a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light over an entire circular disc in the sky. The radius of the disc depends on the wavelength of light, with red light being scattered over a larger angle than blue light. Over most of the disc, scattered light at all wavelengths overlaps, resulting in white light which brightens the sky. At the edge, the wavelength dependence of the scattering gives rise to the rainbow. The light of a primary rainbow arc is 96% polarised tangential to the arc. The light of the second arc is 90% polarised.


Number of colours in a spectrum or a rainbow

A
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
obtained using a glass prism and a point source is a continuum of wavelengths without bands. The number of colours that the human eye is able to distinguish in a spectrum is in the order of 100. Accordingly, the Munsell colour system (a 20th-century system for numerically describing colours, based on equal steps for human visual perception) distinguishes 100 hues. The apparent discreteness of main colours is an artefact of human perception and the exact number of main colours is a somewhat arbitrary choice. Newton, who admitted his eyes were not very critical in distinguishing colours, originally (1672) divided the spectrum into five main colours:
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondar ...
,
yellow Yellow is the color between green and orange on the spectrum of light. It is evoked by light with a dominant wavelength of roughly 575585 nm. It is a primary color in subtractive color systems, used in painting or color printing. In the R ...
,
green Green is the color between cyan and yellow on the visible spectrum. It is evoked by light which has a dominant wavelength of roughly 495570 Nanometre, nm. In subtractive color systems, used in painting and color printing, it is created by ...
,
blue Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when obs ...
and
violet Violet may refer to: Common meanings * Violet (color), a spectral color with wavelengths shorter than blue * One of a list of plants known as violet, particularly: ** ''Viola'' (plant), a genus of flowering plants Places United States * Viol ...
. Later he included orange and
indigo Indigo is a deep color close to the color wheel blue (a primary color in the RGB color space), as well as to some variants of ultramarine, based on the ancient dye of the same name. The word "indigo" comes from the Latin word ''indicum'', m ...
, giving seven main colours by analogy to the number of notes in a musical scale.Isaac Newton, ''Optice: Sive de Reflexionibus, Refractionibus, Inflexionibus & Coloribus Lucis Libri Tres,'' Propositio II, Experimentum VII, edition 1740 Newton chose to divide the visible spectrum into seven colours out of a belief derived from the beliefs of the
ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
sophists, who thought there was a connection between the colours, the musical notes, the known objects in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
, and the days of the week. Scholars have noted that what Newton regarded at the time as "blue" would today be regarded as
cyan Cyan () is the color between green and blue on the visible spectrum of light. It is evoked by light with a predominant wavelength between 490 and 520 nm, between the wavelengths of green and blue. In the subtractive color system, or CMYK color ...
, and what Newton called "indigo" would today be considered
blue Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when obs ...
. The colour pattern of a rainbow is different from a spectrum, and the colours are less saturated. There is spectral smearing in a rainbow owing to the fact that for any particular wavelength, there is a distribution of exit angles, rather than a single unvarying angle. In addition, a rainbow is a blurred version of the bow obtained from a point source, because the disk diameter of the sun (0.5°) cannot be neglected compared to the width of a rainbow (2°). 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 ''rainbow'' is used inaccurately to mean ''spectrum'', it is the number of main colours in the spectrum. The
question A question is an utterance which serves as a request for information. Questions are sometimes distinguished from interrogatives, which are the grammar, grammatical forms typically used to express them. Rhetorical questions, for instance, are inte ...
of whether everyone sees seven colours in a rainbow is related to the idea of
linguistic relativity The hypothesis of linguistic relativity, also known as the Sapir–Whorf hypothesis , the Whorf hypothesis, or Whorfianism, is a principle suggesting that the structure of a language affects its speakers' world view, worldview or cognition, and ...
. 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.


Explanation

When sunlight encounters a raindrop, part of the light is reflected and the rest enters the raindrop. The light is refracted at the surface of the raindrop. When this light hits the back of the raindrop, some of it is reflected off the back. When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop. (The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow.) The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°. This angle is independent of the size of the drop, but does depend on its
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
. 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. The reason the returning light is most intense at about 42° is that this is a turning point – light hitting the outermost ring of the drop gets returned at less than 42°, as does the light hitting the drop nearer to its centre. There is a circular band of light that all gets returned right around 42°. If the Sun were a laser emitting parallel, monochromatic rays, then the
luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
(brightness) of the bow would tend toward infinity at this angle (ignoring interference effects). (See Caustic (optics).) But since the Sun's luminance is finite and its rays are not all parallel (it covers about half a degree of the sky) the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, and hence its colour. This effect is called
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
. Blue light (shorter wavelength) is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside. The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. (A "rainbow" formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow.) The light at the back of the raindrop does not undergo
total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
, and some light does emerge from the back. However, light coming out the back of the raindrop does not create a rainbow between the observer and the Sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow. A rainbow does not exist at one particular location. Many rainbows exist; however, only one can be seen depending on the particular observer's viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. This light is what constitutes the rainbow for that observer. The whole system composed by the Sun's rays, the observer's head, and the (spherical) water drops has an axial symmetry around the axis through the observer's head and parallel to the Sun's rays. The rainbow is curved because the set of all the raindrops that have the right angle between the observer, the drop, and the Sun, lie on a cone pointing at the sun with the observer at the tip. The base of the cone forms a circle at an angle of 40–42° to the line between the observer's head and their shadow but 50% or more of the circle is below the horizon, unless the observer is sufficiently far above the earth's surface to see it all, for example in an aeroplane (see below). Alternatively, an observer with the right vantage point may see the full circle in a fountain or waterfall spray.


Mathematical derivation

It is possible to determine the perceived angle which the rainbow subtends as follows. Given a spherical raindrop, and defining the perceived angle of the rainbow as , and the angle of the internal reflection as , then the angle of incidence of the Sun's rays with respect to the drop's surface normal is . Since the angle of refraction is ,
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
gives us :, where is the refractive index of water. Solving for , we get :. The rainbow will occur where the angle is maximum with respect to the angle . Therefore, from
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
, we can set , and solve for , which yields :\beta_\text = \arccos\left(\frac\right) \approx 40.2^\circ. Substituting back into the earlier equation for yields ≈ 42° as the radius angle of the rainbow. For red light (wavelength 750nm, based on the dispersion relation of water), the radius angle is 42.5°; for blue light (wavelength 350nm, ), the radius angle is 40.6°.


Variations


Double rainbows

A secondary rainbow, at a greater angle than the primary rainbow, is often visible. The term double rainbow is used when both the primary and secondary rainbows are visible. In theory, all rainbows are double rainbows, but since the secondary bow is always fainter than the primary, it may be too weak to spot in practice. Secondary rainbows are caused by a double reflection of sunlight inside the water droplets. Technically the secondary bow is centred on the sun itself, but since its angular size is more than 90° (about 127° for violet to 130° for red), it is seen on the same side of the sky as the primary rainbow, about 10° outside it at an apparent angle of 50–53°. As a result of the "inside" of the secondary bow being "up" to the observer, the colours appear reversed compared to those of the primary bow. The secondary rainbow is fainter than the primary because more light escapes from two reflections compared to one and because the rainbow itself is spread over a greater area of the sky. Each rainbow reflects white light inside its coloured bands, but that is "down" for the primary and "up" for the secondary. The dark area of unlit sky lying between the primary and secondary bows is called Alexander's band, after Alexander of Aphrodisias, who first described it.


Twinned rainbow

Unlike a double rainbow that consists of two separate and concentric rainbow arcs, the very rare twinned rainbow appears as two rainbow arcs that split from a single base. The colours in the second bow, rather than reversing as in a secondary rainbow, appear in the same order as the primary rainbow. A "normal" secondary rainbow may be present as well. Twinned rainbows can look similar to, but should not be confused with supernumerary bands. The two phenomena may be told apart by their difference in colour profile: supernumerary bands consist of subdued pastel hues (mainly pink, purple and green), while the twinned rainbow shows the same spectrum as a regular rainbow. The cause of a twinned rainbow is 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. Meanwhile, the even rarer case of a rainbow split into three branches was observed and photographed in nature.


Full-circle rainbow

In theory, every rainbow is a circle, but from the ground, usually only its upper half can be seen. Since the rainbow's centre is diametrically opposed to the Sun's position in the sky, more of the circle comes into view as the sun approaches the horizon, meaning that the largest section of the circle normally seen is about 50% during sunset or sunrise. Viewing the rainbow's lower half requires the presence of water droplets ''below'' the observer's horizon, as well as sunlight that is able to reach them. These requirements are not usually met when the viewer is at ground level, either because droplets are absent in the required position, or because the sunlight is obstructed by the landscape behind the observer. From a high viewpoint such as a high building or an aircraft, however, the requirements can be met and the full-circle rainbow can be seen. Like a partial rainbow, the circular rainbow can have a secondary bow or supernumerary bows as well. It is possible to produce the full circle when standing on the ground, for example by spraying a water mist from a garden hose while facing away from the sun. A circular rainbow should not be confused with the glory, which is much smaller in diameter and is created by different optical processes. In the right circumstances, a glory and a (circular) rainbow or
fog bow Fog is a visible aerosol consisting of tiny water drop (liquid), droplets or ice crystals suspended in the air at or near the Earth, Earth's land, surface. Reprint from Fog can be considered a type of low-lying cloud usually resembling str ...
can occur together. Another atmospheric phenomenon that may be mistaken for a "circular rainbow" is the
22° halo A 22° halo is an atmospheric optical phenomenon that consists of a halo with an apparent radius of approximately 22° around the Sun or Moon. When visible around the Moon, it is also known as a moon ring or winter halo. It forms as sunlight o ...
, which is caused by ice crystals rather than liquid water droplets, and is located around the Sun (or Moon), not opposite it.


Supernumerary rainbows

In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i.e., inside the primary bow or, much more rarely, outside the secondary. These extra bands are called ''supernumerary rainbows'' or ''supernumerary bands''; together with the rainbow itself the phenomenon is also known as a ''stacker rainbow''. The supernumerary bows are slightly detached from the main bow, become successively fainter along with their distance from it, and have pastel colours (consisting mainly of pink, purple and green hues) rather than the usual spectrum pattern. The effect becomes apparent when water droplets are involved that have a diameter of about 1 mm or less; the smaller the droplets are, the broader the supernumerary bands become, and the less saturated their colours. Due to their origin in small droplets, supernumerary bands tend to be particularly prominent in fogbows. Supernumerary rainbows cannot be explained using classical geometric
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
. The alternating faint bands are caused by
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extra ...
between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
, reinforcing each other through constructive interference, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interference, and creating a gap. Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow. Supernumerary rainbows are clearest when raindrops are small and of uniform size. The very existence of supernumerary rainbows was historically a first indication of the
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
nature of light, and the first explanation was provided by Thomas Young in 1804.


Reflected rainbow, reflection rainbow

When a rainbow appears above a body of water, two complementary mirror bows may be seen below and above the horizon, originating from different light paths. Their names are slightly different. A reflected rainbow may appear in the water surface below the horizon. The sunlight is first deflected by the raindrops, and then reflected off the body of water, before reaching the observer. The reflected rainbow is frequently visible, at least partially, even in small puddles. A reflection rainbow may be produced where sunlight reflects off a body of water before reaching the raindrops, if the water body is large, quiet over its entire surface, and close to the rain curtain. The reflection rainbow appears above the horizon. It intersects the normal rainbow at the horizon, and its arc reaches higher in the sky, with its centre as high above the horizon as the normal rainbow's centre is below it. 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. Up to eight separate bows may be distinguished if the reflected and reflection rainbows happen to occur simultaneously: The normal (non-reflection) primary and secondary bows above the horizon (1, 2) with their reflected counterparts below it (3, 4), and the reflection primary and secondary bows above the horizon (5, 6) with their reflected counterparts below it (7, 8).


Monochrome rainbow

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


Higher-order rainbows

In addition to the common primary and secondary rainbows, it is also possible for rainbows of higher orders to form. The order of a rainbow is determined by the number of light reflections inside the water droplets that create it: One reflection results in the first-order or ''primary'' rainbow; two reflections create the second-order or ''secondary'' rainbow. More internal reflections cause bows of higher orders—theoretically unto infinity. As more and more light is lost with each internal reflection, however, each subsequent bow becomes progressively dimmer and therefore increasingly difficult to spot. An additional challenge in observing the third-order (or ''tertiary'') and fourth-order (''quaternary'') rainbows is their location in the direction of the sun (about 40° and 45° from the sun, respectively), causing them to become drowned in its glare. For these reasons, naturally occurring rainbows of an order higher than 2 are rarely visible to the naked eye. Nevertheless, sightings of the third-order bow in nature have been reported, and in 2011 it was photographed definitively for the first time. Shortly after, the fourth-order rainbow was photographed as well, and in 2014 the first ever pictures of the fifth-order (or ''quinary'') rainbow 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 (1808–1882) depicted angular positions up to the 19th-order rainbow, a pattern he called a "rose of rainbows".J.D. Walker, "Mysteries of rainbows, notably their rare supernumerary arcs," Sci. Am. 242(6), 174–184 (1980). In the laboratory, it is possible to observe higher-order rainbows by using extremely bright and well collimated light produced by
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
s. Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam. Tertiary and quaternary rainbows should not be confused with "triple" and "quadruple" rainbows—terms sometimes erroneously used to refer to the—much more common—supernumerary bows and reflection rainbows.


Rainbows under moonlight

Like most atmospheric optical phenomena, rainbows can be caused by light from the Sun, but also from the Moon. In case of the latter, the rainbow is referred to as a lunar rainbow or moonbow. They are much dimmer and rarer than solar rainbows, requiring the Moon to be near-full in order for them to be seen. For the same reason, moonbows are often perceived as white and may be thought of as monochrome. The full spectrum is present, however, but the human eye is not normally sensitive enough to see the colours. Long exposure photographs will sometimes show the colour in this type of rainbow.


Fogbow

Fogbows form in the same way as rainbows, but they are formed by much smaller cloud and fog droplets that diffract light extensively. They are almost white with faint reds on the outside and blues inside; often one or more broad supernumerary bands can be discerned inside the inner edge. The colours are dim because the bow in each colour is very broad and the colours overlap. Fogbows are commonly seen over water when air in contact with the cooler water is chilled, but they can be found anywhere if the fog is thin enough for the sun to shine through and the sun is fairly bright. They are very large—almost as big as a rainbow and much broader. They sometimes appear with a glory at the bow's centre. Fog bows should not be confused with ice halos, which are very common around the world and visible much more often than rainbows (of any order), yet are unrelated to rainbows.


Sleetbow

A sleetbow forms in the same way as a typical rainbow, with the exception that it occurs when light passes through falling sleet (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 December 21, 2012. Just like regular rainbows, these can also come in various forms, with a
monochrome A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, monochrom ...
sleetbow being documented on January 7, 2016 in Valparaiso, Indiana.


Circumhorizontal and circumzenithal arcs

The circumzenithal and circumhorizontal arcs are two related optical phenomena similar in appearance to a rainbow, but unlike the latter, their origin lies in light refraction through hexagonal ice crystals rather than liquid water droplets. This means that they are not rainbows, but members of the large family of halos. Both arcs are brightly coloured ring segments centred on the
zenith The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
, but in different positions in the sky: The circumzenithal arc is notably curved and located high above the Sun (or Moon) with its convex side pointing downwards (creating the impression of an "upside down rainbow"); the circumhorizontal arc runs much closer to the horizon, is more straight and located at a significant distance below the Sun (or Moon). Both arcs have their red side pointing towards the Sun and their violet part away from it, meaning the circumzenithal arc is red on the bottom, while the circumhorizontal arc is red on top. The circumhorizontal arc is sometimes referred to by the misnomer "fire rainbow". In order to view it, the Sun or Moon must be at least 58° above the horizon, making it a rare occurrence at higher latitudes. The circumzenithal arc, visible only at a solar or lunar elevation of less than 32°, is much more common, but often missed since it occurs almost directly overhead.


Extraterrestrial rainbows

It has been suggested that rainbows might exist on
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
's moon
Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...
, as it has a wet surface and humid clouds. The radius of a Titan rainbow would be about 49° instead of 42°, because the fluid in that cold environment is methane instead of water. Although visible rainbows may be rare due to Titan's hazy skies,
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
rainbows may be more common, but an observer would need infrared
night vision goggles A night-vision device (NVD), also known as a night optical/observation device (NOD), night-vision goggle (NVG), is an optoelectronic device that allows visualization of images in low levels of light, improving the user's night vision. The dev ...
to see them.


Rainbows with different materials

Droplets (or spheres) composed of materials with different refractive indices than plain water produce rainbows with different radius angles. Since salt water has a higher refractive index, a sea spray bow doesn't perfectly align with the ordinary rainbow, if seen at the same spot. Tiny plastic or glass marbles may be used in road marking as a reflectors to enhance its visibility by drivers at night. Due to a much higher refractive index, rainbows observed on such marbles have a noticeably smaller radius. One can easily reproduce such phenomena by sprinkling liquids of different refractive indices in the air, as illustrated in the photo. The displacement of the rainbow due to different refractive indices can be pushed to a peculiar limit. For a material with a refractive index larger than 2, there is no angle fulfilling the requirements for the first order rainbow. For example, the index of refraction of
diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the Chemical stability, chemically stable form of car ...
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 , where is a
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...
, the critical incidence angle for times internally reflected rays escapes the domain ,\frac/math>. This results in a rainbow of the -th order shrinking to the antisolar point and vanishing.


Scientific history

The classical Greek scholar
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
(384–322 BC) was first to devote serious attention to the rainbow. According to Raymond L. Lee and Alistair B. Fraser, "Despite its many flaws and its appeal to Pythagorean numerology, Aristotle's qualitative explanation showed an inventiveness and relative consistency that was unmatched for centuries. After Aristotle's death, much rainbow theory consisted of reaction to his work, although not all of this was uncritical." In Book I of '' Naturales Quaestiones'' (c. 65 AD), the
Roman Roman or Romans most often refers to: *Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a letter ...
philosopher
Seneca the Younger Lucius Annaeus Seneca the Younger (; 65 AD), usually known mononymously as Seneca, was a Stoic philosopher of Ancient Rome, a statesman, dramatist, and, in one work, satirist, from the post-Augustan age of Latin literature. Seneca was born in ...
discusses various theories of the formation of rainbows extensively, including those of Aristotle. He notices that rainbows appear always opposite to the Sun, that they appear in water sprayed by a rower, in the water spat by a fuller on clothes stretched on pegs or by water sprayed through a small hole in a burst pipe. He even speaks of rainbows produced by small rods (virgulae) of glass, anticipating Newton's experiences with prisms. He takes into account two theories: one, that the rainbow is produced by the Sun reflecting in each water drop, the other, that it is produced by the Sun reflected in a cloud shaped like a
concave mirror A curved mirror is a mirror with a curved reflecting surface. The surface may be either ''convex'' (bulging outward) or ''concave'' (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are ...
; he favours the latter. He also discusses other phenomena related to rainbows: the mysterious "virgae" (rods), halos and parhelia. According to Hüseyin Gazi Topdemir, the Arab physicist and
polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
Ibn al-Haytham Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
(Alhazen; 965–1039), attempted to provide a scientific explanation for the rainbow phenomenon. In his ''Maqala fi al-Hala wa Qaws Quzah'' (''On the Rainbow and Halo''), al-Haytham "explained the formation of rainbow as an image, which forms at a concave mirror. If the rays of light coming from a farther light source reflect to any point on axis of the concave mirror, they form concentric circles in that point. When it is supposed that the sun as a farther light source, the eye of viewer as a point on the axis of mirror and a cloud as a reflecting surface, then it can be observed the concentric circles are forming on the axis." He was not able to verify this because his theory that "light from the sun is reflected by a cloud before reaching the eye" did not allow for a possible
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
al verification. This explanation was repeated by Averroes, and, though incorrect, provided the groundwork for the correct explanations later given by Kamāl al-Dīn al-Fārisī in 1309 and, independently, by Theodoric of Freiberg (c. 1250–c. 1311)—both having studied al-Haytham's ''
Book of Optics The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...
''. Ibn al-Haytham's contemporary, the Persian philosopher and polymath Ibn Sīnā (Avicenna; 980–1037), provided an alternative explanation, writing "that the bow is not formed in the dark cloud but rather in the very thin mist lying between the cloud and the sun or observer. The cloud, he thought, serves simply as the background of this thin substance, much as a quicksilver lining is placed upon the rear surface of the glass in a mirror. Ibn Sīnā would change the place not only of the bow, but also of the colour formation, holding the iridescence to be merely a subjective sensation in the eye." This explanation, however, was also incorrect. Ibn Sīnā's account accepts many of Aristotle's arguments on the rainbow. In Song Dynasty China (960–1279), a polymath
scholar-official The scholar-officials, also known as literati, scholar-gentlemen or scholar-bureaucrats (), were government officials and prestigious scholars in Chinese society, forming a distinct social class. Scholar-officials were politicians and governmen ...
named
Shen Kuo Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (存中) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁),Yao (2003), 544. was a Chinese polymathic scientist and statesman of the Song dynasty (960–1279). Shen wa ...
(1031–1095) hypothesised—as a certain Sun Sikong (1015–1076) did before him—that rainbows were formed by a phenomenon of sunlight encountering droplets of rain in the air. Paul Dong writes that Shen's explanation of the rainbow as a phenomenon of atmospheric refraction "is basically in accord with modern scientific principles." According to Nader El-Bizri, the Persian astronomer, Qutb al-Din al-Shirazi (1236–1311), gave a fairly accurate explanation for the rainbow phenomenon. This was elaborated on by his student, Kamāl al-Dīn al-Fārisī (1267–1319), who gave a more mathematically satisfactory explanation of the rainbow. He "proposed a model where the ray of light from the sun was refracted twice by a water droplet, one or more reflections occurring between the two refractions." An experiment with a water-filled glass sphere was conducted and al-Farisi showed the additional refractions due to the glass could be ignored in his model. As he noted in his ''Kitab Tanqih al-Manazir'' (''The Revision of the Optics''), al-Farisi used a large clear vessel of glass in the shape of a sphere, which was filled with water, in order to have an experimental large-scale model of a rain drop. He then placed this model within a camera obscura that has a controlled
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An opt ...
for the introduction of light. He projected light unto the sphere and ultimately deduced through several trials and detailed observations of reflections and refractions of light that the colours of the rainbow are phenomena of the decomposition of light. In Europe, Ibn al-Haytham's ''Book of Optics'' was translated into Latin and studied by Robert Grosseteste. His work on light was continued by
Roger Bacon Roger Bacon (; la, Rogerus or ', also '' Rogerus''; ), also known by the scholastic accolade ''Doctor Mirabilis'', was a medieval English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through empiri ...
, who wrote in his '' Opus Majus'' of 1268 about experiments with light shining through crystals and water droplets showing the colours of the rainbow. In addition, Bacon was the first to calculate the angular size of the rainbow. He stated that the rainbow summit can not appear higher than 42° above the horizon. Theodoric of Freiberg is known to have given an accurate theoretical explanation of both the primary and secondary rainbows in 1307. He explained the primary rainbow, noting that "when sunlight falls on individual drops of moisture, the rays undergo two refractions (upon ingress and egress) and one reflection (at the back of the drop) before transmission into the eye of the observer." He explained the secondary rainbow through a similar analysis involving two refractions and two reflections. Descartes' 1637 treatise, '' Discourse on Method,'' further advanced this explanation. Knowing that the size of raindrops did not appear to affect the observed rainbow, he experimented with passing rays of light through a large glass sphere filled with water. By measuring the angles that the rays emerged, he concluded that the primary bow was caused by a single internal reflection inside the raindrop and that a secondary bow could be caused by two internal reflections. He supported this conclusion with a derivation of the law of
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
(subsequently to, but independently of, Snell) and correctly calculated the angles for both bows. His explanation of the colours, however, was based on a mechanical version of the traditional theory that colours were produced by a modification of white light. Isaac Newton demonstrated that white light was composed of the light of all the colours of the rainbow, which a glass
prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
could separate into the full spectrum of colours, rejecting the theory that the colours were produced by a modification of white light. He also showed that red light is refracted less than blue light, which led to the first scientific explanation of the major features of the rainbow. Newton's corpuscular theory of light was unable to explain supernumerary rainbows, and a satisfactory explanation was not found until Thomas Young realised that light behaves as a wave under certain conditions, and can interfere with itself. Young's work was refined in the 1820s by George Biddell Airy, who explained the dependence of the strength of the colours of the rainbow on the size of the water droplets. Modern physical descriptions of the rainbow are based on
Mie scattering The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the f ...
, work published by Gustav Mie in 1908. Advances in computational methods and optical theory continue to lead to a fuller understanding of rainbows. For example, Nussenzveig provides a modern overview.


Experiments

Experiments on the rainbow phenomenon using artificial raindrops, i.e. water-filled spherical flasks, go back at least to Theodoric of Freiberg in the 14th century. Later, also Descartes studied the phenomenon using a Florence flask. A flask experiment known as Florence's rainbow is still often used today as an imposing and intuitively accessible demonstration experiment of the rainbow phenomenon.“Florence's Rainbow”, Harvard Natural Sciences Lecture Demonstrations
link
“Rainbow: Refraction of white light by a liquid sphere.”, U.C. Berkeley Physics Lecture Demonstrations
link
“The Rainbow,”J.B. Calvert

, retrieved: 10/01/2016
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,“Revisiting the round bottom flask rainbow experiment.”, M. Selmke and S. Selmke, arXiv
link
Pictures and Raytracings under "Alexander's dark band (or bright band?)", M. Selmke
link
including slightly changed rainbow angles and a splitting of the rainbow orders. A very similar experiment consists in using a cylindrical glass vessel filled with water or a solid transparent cylinder and illuminated either parallel to the circular base (i.e. light rays remaining at a fixed height while they transit the cylinder)G. Casini and A. Covello, “The ”rainbow” in the drop,” Am. J. Phys. 80(11), 1027–1034 (2012).“Primary and Secondary Bow of a Rainbow”, U.C. Berkeley Physics Lecture Demonstrations
link
or under an angle to the base. Under these latter conditions the rainbow angles change relative to the natural phenomenon since the effective index of refraction of water changes (Bravais' index of refraction for inclined rays applies). Other experiments use small liquid drops, see text above.


Culture and mythology

Rainbows occur frequently in mythology, and have been used in the arts. The first literary occurrence of a rainbow is in the
Book of Genesis The Book of Genesis (from Greek ; Hebrew: בְּרֵאשִׁית ''Bəreʾšīt'', "In hebeginning") is the first book of the Hebrew Bible and the Christian Old Testament. Its Hebrew name is the same as its first word, ( "In the beginning") ...
chapter 9, as part of the flood story of
Noah Noah ''Nukh''; am, ኖህ, ''Noḥ''; ar, نُوح '; grc, Νῶε ''Nôe'' () is the tenth and last of the pre-Flood patriarchs in the traditions of Abrahamic religions. His story appears in the Hebrew Bible (Book of Genesis, chapters 5– ...
, where it is a sign of God's covenant to never destroy all life on Earth with a global flood again. In
Norse mythology Norse, Nordic, or Scandinavian mythology is the body of myths belonging to the North Germanic peoples, stemming from Old Norse religion and continuing after the Christianization of Scandinavia, and into the Nordic folklore of the modern period ...
, the rainbow bridge
Bifröst In Norse mythology, Bifröst (), also called Bilröst, is a burning rainbow bridge that reaches between Midgard (Earth) and Asgard, the realm of the gods. The bridge is attested as ''Bilröst'' in the ''Poetic Edda''; compiled in the 13th centur ...
connects the world of men ( Midgard) and the realm of the gods ( Asgard).
Cuchavira Cuchavira or Cuchaviva is the rainbow deity, protector of working women and the sick in the religion of the Muisca. The Muisca and their confederation were one of the advanced civilizations of the Americas and in the fertile intermontane valley t ...
was the god of the rainbow for the Muisca in present-day
Colombia Colombia (, ; ), officially the Republic of Colombia, is a country in South America with insular regions in North America—near Nicaragua's Caribbean coast—as well as in the Pacific Ocean. The Colombian mainland is bordered by the Car ...
and when the regular rains on the Bogotá savanna were over, the people thanked him offering
gold Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
,
snail A snail is, in loose terms, a shelled gastropod. The name is most often applied to land snails, terrestrial pulmonate gastropod molluscs. However, the common name ''snail'' is also used for most of the members of the molluscan class Gastro ...
s and small
emerald Emerald is a gemstone and a variety of the mineral beryl (Be3Al2(SiO3)6) colored green by trace amounts of chromium or sometimes vanadium.Hurlbut, Cornelius S. Jr. and Kammerling, Robert C. (1991) ''Gemology'', John Wiley & Sons, New York, p ...
s. Some forms of
Tibetan Buddhism Tibetan Buddhism (also referred to as Indo-Tibetan Buddhism, Lamaism, Lamaistic Buddhism, Himalayan Buddhism, and Northern Buddhism) is the form of Buddhism practiced in Tibet and Bhutan, where it is the dominant religion. It is also in majo ...
or
Dzogchen Dzogchen (, "Great Perfection" or "Great Completion"), also known as ''atiyoga'' ( utmost yoga), is a tradition of teachings in Indo-Tibetan Buddhism and Yungdrung Bon aimed at discovering and continuing in the ultimate ground of existence. ...
reference a rainbow body. The Irish leprechaun's secret hiding place for his pot of gold is usually said to be at the end of the rainbow. This place is appropriately impossible to reach, because the rainbow is an optical effect which cannot be approached. In
Greek mythology A major branch of classical mythology, Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of Ancient Greek folklore. These stories concern the Cosmogony, origin and Cosmology#Metaphysical co ...
, the goddess Iris is the personification of the rainbow, a messenger goddess who, like the rainbow, connects the mortal world with the gods through messages. Rainbows appear in heraldry - in heraldry the rainbow proper consists of 4 bands of colour ( Or,
Gules In heraldry, gules () is the tincture with the colour red. It is one of the class of five dark tinctures called "colours", the others being azure (blue), sable (black), vert (green) and purpure (purple). In engraving, it is sometimes depict ...
,
Vert Vert or Verts may refer to: * Vert (heraldry), the colour green in heraldry * Vert (music producer) (born 1972), pseudonym of Adam Butler, an English music producer * Vert (river), in southern France * Vert (sport), a competition in extreme vers ...
, Argent) with the ends resting on clouds. Generalised examples in coat of arms include those of the towns of Regen and
Pfreimd Pfreimd is a town in the district of Schwandorf, in Bavaria, Germany. It is situated on the river Naab, 19 km north of Schwandorf, and 20 km south of Weiden in der Oberpfalz. It is also close to the border with the Czech Republic. May ...
, both in Bavaria, Germany; of Bouffémont, France; and of the
69th Infantry Regiment (New York) The 69th New York Infantry Regiment is an infantry regiment of the United States Army. It is from New York City, part of the New York Army National Guard. It is known as the "Fighting Sixty-Ninth", a name said to have been given by Robert E ...
of the United States
Army National Guard The Army National Guard (ARNG), in conjunction with the Air National Guard, is an organized Militia (United States), militia force and a Reserve components of the United States Armed Forces, federal military reserve force of the United States A ...
.
Rainbow flag A rainbow flag is a multicolored flag consisting of the colors of the rainbow. The designs differ, but many of the colors are based on the spectral colors of the visible light spectrum. The LGBT flag introduced in 1978 is the most recognized u ...
s have been used for centuries. It was a symbol of the Cooperative movement in the
German Peasants' War The German Peasants' War, Great Peasants' War or Great Peasants' Revolt (german: Deutscher Bauernkrieg) was a widespread popular revolt in some German-speaking areas in Central Europe from 1524 to 1525. It failed because of intense oppositio ...
in the 16th century, of peace in Italy, and of gay pride and LGBT social movements since the 1970s. In 1994, Archbishop
Desmond Tutu Desmond Mpilo Tutu (7 October 193126 December 2021) was a South African Anglican bishop and theologian, known for his work as an anti-apartheid and human rights activist. He was Bishop of Johannesburg from 1985 to 1986 and then Archbishop ...
and President
Nelson Mandela Nelson Rolihlahla Mandela (; ; 18 July 1918 – 5 December 2013) was a South African Internal resistance to apartheid, anti-apartheid activist who served as the President of South Africa, first president of South Africa from 1994 to 1 ...
described newly democratic post-
apartheid Apartheid (, especially South African English: , ; , "aparthood") was a system of institutionalised racial segregation that existed in South Africa and South West Africa (now Namibia) from 1948 to the early 1990s. Apartheid was ...
South Africa as the rainbow nation. The rainbow has also been used in technology product logos, including the
Apple computer Apple Inc. is an American multinational technology company headquartered in Cupertino, California, United States. Apple is the largest technology company by revenue (totaling in 2021) and, as of June 2022, is the world's biggest company b ...
logo. Many political alliances spanning multiple political parties have called themselves a " Rainbow Coalition". Pointing at rainbows has been considered a taboo in many cultures. In Saudi Arabia (and some other countries), authorities seize rainbow-coloured children's clothing and toys (such as hats, hair clips, and pencil cases, not just flags), which they claim encourage homosexuality, and selling such is illegal.


See also

* Atmospheric optics *
Circumzenithal arc The circumzenithal arc, also called the circumzenith arc (CZA), upside-down rainbow, and the Bravais arc,"Mémoire sur les halos et les phénomènes optiques qui les accompagnent", J. de l' École Royale Polytechnique 31(18), 1-270, A. Bravais, ...
* Circumhorizontal arc * Iridescent colours in soap bubbles *
Sun dog A sun dog (or sundog) or mock sun, also called a parhelion (plural parhelia) in meteorology, is an atmospheric optical phenomenon that consists of a bright spot to one or both sides of the Sun. Two sun dogs often flank the Sun within a 22° ...
*
Fog bow Fog is a visible aerosol consisting of tiny water drop (liquid), droplets or ice crystals suspended in the air at or near the Earth, Earth's land, surface. Reprint from Fog can be considered a type of low-lying cloud usually resembling str ...
* Moonbow


Notes


References


Further reading

* * * (Large format handbook for the Summer 1976 exhibition ''The Rainbow Art Show'' which took place primarily at the De Young Museum but also at other museums. The book is divided into seven sections, each coloured a different colour of the rainbow.) * * * * * *


External links


The Mathematics of Rainbows
article from the
American mathematical society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Interactive simulation of light refraction in a drop (java applet)

Rainbow seen through infrared filter and through ultraviolet filter


– Description of multiple types of bows, including: "bows that cross, red bows, twinned bows, coloured fringes, dark bands, spokes", etc. *
Creating Circular and Double Rainbows!
– video explanation of basics, shown artificial rainbow at night, second rainbow and circular one. {{Authority control Atmospheric optical phenomena Lucky symbols Heraldic charges LGBT symbols Atmospheric sciences