![Double-alaskan-rainbow](https://upload.wikimedia.org/wikipedia/commons/5/5c/Double-alaskan-rainbow.jpg)
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 Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
,
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
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 ...
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
![WhereRainbowRises](https://upload.wikimedia.org/wikipedia/commons/2/27/WhereRainbowRises.jpg)
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 ...
, 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 wh ...
.
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
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles: altitude and azimuth.
Therefore, the horizontal coordinate system is sometimes called as the ...
. 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.
![Steam Phase eruption of Castle geyser with double rainbow](https://upload.wikimedia.org/wikipedia/commons/4/49/Steam_Phase_eruption_of_Castle_geyser_with_double_rainbow.jpg)
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
A moonbow (also known as a moon rainbow or lunar rainbow) is a rainbow produced by moonlight rather than direct sunlight. Other than the difference in the light source, its formation is the same as for a solar rainbow: It is caused by the refract ...
, 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
In colorimetry, the Munsell color system is a color space that specifies colors based on three properties of color: hue (basic color), chroma (color intensity), and value (lightness). It was created by Professor Albert H. Munsell in the first ...
(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
Orange most often refers to:
*Orange (fruit), the fruit of the tree species '' Citrus'' × ''sinensis''
** Orange blossom, its fragrant flower
*Orange (colour), from the color of an orange, occurs between red and yellow in the visible spectrum
* ...
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 ...
sophist
A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...
s, 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 ...
.
![Prism compare rainbow 01](https://upload.wikimedia.org/wikipedia/commons/f/f6/Prism_compare_rainbow_01.png)
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
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 ...
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)
In optics, a caustic or caustic network is the envelope of light rays which have been reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to ...
.) 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
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. 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
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines con ...
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
![Raindrop optics](https://upload.wikimedia.org/wikipedia/commons/e/ee/Raindrop_optics.jpg)
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
:
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
![Rainbow_principle](https://upload.wikimedia.org/wikipedia/commons/7/71/Rainbow_principle.svg)
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
Alexander's band or Alexander's dark band is an optical phenomenon associated with rainbows which was named after Alexander of Aphrodisias who first described this phenomenon in Aphrodisias, ''Commentary on Book IV of Aristotle's'' Meteoro ...
, after
Alexander of Aphrodisias
Alexander of Aphrodisias ( grc-gre, Ἀλέξανδρος ὁ Ἀφροδισιεύς, translit=Alexandros ho Aphrodisieus; AD) was a Peripatetic school, Peripatetic philosopher and the most celebrated of the Ancient Greek Commentaries on Aristo ...
, 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.
![Circular rainbow](https://upload.wikimedia.org/wikipedia/commons/3/38/Circular_rainbow.jpg)
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 droplets or ice crystals suspended in the air at or near the Earth's surface. Reprint from Fog can be considered a type of low-lying cloud usually resembling stratus, and is heavily infl ...
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
Ice crystals are solid ice exhibiting atomic ordering on various length scales and include hexagonal columns, hexagonal plates, dendritic crystals, and diamond dust.
Formation
The hugely symmetric shapes are due to depositional growth, na ...
rather than liquid water droplets, and is located around the Sun (or Moon), not opposite it.
Supernumerary rainbows
![Supernumerary-rainbows-jb](https://upload.wikimedia.org/wikipedia/commons/2/24/Supernumerary-rainbows-jb.jpg)
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 extr ...
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
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through
destructive interference
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
, 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
![ReflectionRainbow](https://upload.wikimedia.org/wikipedia/commons/c/c8/ReflectionRainbow.jpg)
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
![Monochrome rainbow](https://upload.wikimedia.org/wikipedia/commons/9/96/Monochrome_rainbow.jpg)
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
A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction pr ...
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
![Moonbow at lower Yosemite fall](https://upload.wikimedia.org/wikipedia/commons/1/1b/Moonbow_at_lower_Yosemite_fall.jpg)
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
A moonbow (also known as a moon rainbow or lunar rainbow) is a rainbow produced by moonlight rather than direct sunlight. Other than the difference in the light source, its formation is the same as for a solar rainbow: It is caused by the refract ...
. 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
![Fogbow spectre and glory filtered](https://upload.wikimedia.org/wikipedia/commons/5/50/Fogbow_spectre_and_glory_filtered.jpg)
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
![Sleetbow](https://upload.wikimedia.org/wikipedia/commons/4/46/Sleetbow.jpeg)
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
![Circumzenithalarc](https://upload.wikimedia.org/wikipedia/commons/8/81/Circumzenithalarc.jpg)
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
Ice crystals are solid ice exhibiting atomic ordering on various length scales and include hexagonal columns, hexagonal plates, dendritic crystals, and diamond dust.
Formation
The hugely symmetric shapes are due to depositional growth, na ...
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
A circumhorizontal arc is an optical phenomenon that belongs to the family of ice halos formed by the refraction of sunlight or moonlight in plate-shaped ice crystals suspended in the atmosphere, typically in cirrus or cirrostratus clouds. In i ...
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, 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
![First order rainbows from water droplets and a sugar solution droplets](https://upload.wikimedia.org/wikipedia/commons/1/19/First_order_rainbows_from_water_droplets_and_a_sugar_solution_droplets.jpg)
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