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= Rainbow =
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Introduction
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A rainbow is an optical phenomenon caused by refraction, internal
reflection and dispersion of light in water droplets resulting in a
continuous spectrum of light appearing in the sky. The rainbow takes
the form of a multicoloured circular arc. Rainbows caused by sunlight
always appear in the section of sky directly opposite the Sun.
Rainbows can be caused by many forms of airborne water. These include
not only rain, but also mist, spray, and airborne dew.
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.
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 clouds and the observer is at a spot with clear sky in
the direction of the Sun. The result is a luminous rainbow that
contrasts with the darkened background. During such good visibility
conditions, the larger but fainter secondary rainbow is often visible.
It appears about 10° outside of the primary rainbow, with inverse
order of colours.
The rainbow effect is also commonly seen near waterfalls or fountains.
In addition, the effect can be artificially created by dispersing
water droplets into the air during a sunny day. Rarely, a moonbow,
lunar rainbow or nighttime rainbow, can be seen on strongly moonlit
nights. As human visual perception for colour is poor in low light,
moonbows are often perceived to be white.
It is difficult to photograph the complete semicircle of a rainbow in
one frame, as this would require an angle of view of 84°. For a 35 mm
camera, a wide-angle lens with a focal length of 19 mm or less would
be required. Now that software for stitching several images into a
panorama is available, images of the entire arc and even secondary
arcs can be created fairly easily from a series of overlapping frames.
From above the Earth such as in an aeroplane, it is sometimes possible
to see a rainbow as a full circle. This phenomenon can be confused
with the glory phenomenon, but a glory is usually much smaller,
covering only 5-20°.
The sky inside a primary rainbow is brighter than the sky outside of
the bow. This is because each raindrop is a sphere and it scatters
light over an entire circular disc in the sky. The radius of the disc
depends on the wavelength of light, with red light being scattered
over a larger angle than blue light. Over most of the disc, scattered
light at all wavelengths overlaps, resulting in white light which
brightens the sky. At the edge, the wavelength dependence of the
scattering gives rise to the rainbow.
The light of a primary rainbow arc is 96% polarised tangential to the
arc. The light of the second arc is 90% polarised.
{{Anchor|The seven colours of the rainbow}}Number of colours in a spectrum or a rainbow
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For colours seen by the human eye, the most commonly cited and
remembered sequence is Isaac Newton's sevenfold red, orange, yellow,
green, blue, indigo and violet, remembered by the mnemonic 'Richard Of
York Gave Battle In Vain,' or as the name of a fictional person (Roy
G. Biv). The initialism is sometimes referred to in reverse order, as
VIBGYOR. More modernly, the rainbow is often divided into red, orange,
yellow, green, cyan, blue and violet. The apparent discreteness of
main colours is an artefact of human perception and the exact number
of main colours is a somewhat arbitrary choice.
Newton, who admitted his eyes were not very critical in distinguishing
colours, originally (1672) divided the spectrum into five main
colours: red, yellow, green, blue and violet. Later he included orange
and indigo, giving seven main colours by analogy to the number of
notes in a musical scale. Newton chose to divide the visible spectrum
into seven colours out of a belief derived from the beliefs of the
ancient Greek sophists, who thought there was a connection between the
colours, the musical notes, the known objects in the Solar System, and
the days of the week. Scholars have noted that what Newton regarded at
the time as "blue" would today be regarded as cyan, what Newton called
"indigo" would today be called blue.
Newton's first colours Red Yellow Green Blue Violet
Newton's later colours Red Orange Yellow Green Blue Indigo Violet
Modern interpretation Red Orange Yellow Green Cyan Blue Violet
The colour pattern of a rainbow is different from a spectrum, and the
colours are less saturated. There is spectral smearing in a rainbow
since, for any particular wavelength, there is a distribution of exit
angles, rather than a single unvarying angle. In addition, a rainbow
is a blurred version of the bow obtained from a point source, because
the disk diameter of the sun (0.5°) cannot be neglected compared to
the width of a rainbow (2°). The number of colour bands of a rainbow
may therefore be different from the number of bands in a spectrum,
especially if the droplets are particularly large or small. Therefore,
the number of colours of a rainbow is variable. If, however, the word
'rainbow' is used inaccurately to mean 'spectrum', it is the number of
main colours in the spectrum.
Moreover, rainbows have bands beyond red and violet in the respective
near infrared and ultraviolet regions, however, these bands are not
visible to humans. Only near frequencies of these regions to the
visible spectrum are included in rainbows, since water and air become
increasingly opaque to these frequencies, scattering the light. The UV
band is sometimes visible to cameras using black and white film.
The question of whether everyone sees seven colours in a rainbow is
related to the idea of linguistic relativity. Suggestions have been
made that there is universality in the way that a rainbow is
perceived. However, more recent research suggests that the number of
distinct colours observed and what these are called depend on the
language that one uses, with people whose language has fewer colour
words seeing fewer discrete colour bands.
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. 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 (brightness) of the bow would
tend toward infinity at this angle if interference effects are ignored
. But since the Sun's luminance is finite and its rays are not all
parallel (it covers about half a degree of the sky) the luminance does
not go to infinity. Furthermore, the amount by which light is
refracted depends upon its wavelength, and hence its colour. This
effect is called dispersion. Blue light (shorter wavelength) is
refracted at a greater angle than red light, but due to the reflection
of light rays from the back of the droplet, the blue light emerges
from the droplet at a smaller angle to the original incident white
light ray than the red light. Due to this angle, blue is seen on the
inside of the arc of the primary rainbow, and red on the outside. The
result of this is not only to give different colours to different
parts of the rainbow, but also to diminish the brightness. (A
"rainbow" formed by droplets of a liquid with no dispersion would be
white, but brighter than a normal rainbow.)
The light at the back of the raindrop does not undergo total internal
reflection, and most of the light emerges from the back. However,
light coming out the back of the raindrop does not create a rainbow
between the observer and the Sun because spectra emitted from the back
of the raindrop do not have a maximum of intensity, as the other
visible rainbows do, and thus the colours blend together rather than
forming a rainbow.
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. Conversely, at lower latitudes near midday
(specifically, when the sun's elevation exceeds 42 degrees) a rainbow
will not be visible against the sky.
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
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, 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°.
Double rainbows
=================
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.See:
*Alexander of Aphrodisias, 'Commentary on Book IV of Aristotle's'
Meteorology (also known as: 'Commentary on Book IV of Aristotle's' De
Meteorologica or 'On Aristotle's' Meteorology 4), commentary 41.
*Raymond L. Lee and Alistair B. Fraser, 'The Rainbow Bridge: Rainbows
in Art, Myth, and Science' (University Park, Pennsylvania:
Pennsylvania State University Press, 2001),
[
https://books.google.com/books?id=kZcCtT1ZeaEC&pg=PA110 pp.
110-111].
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.See:
*
* [
https://www.sciencedaily.com/releases/2012/08/120806151415.htm
"Researchers unlock secret of the rare 'twinned rainbow,' "
'ScienceDaily.com,' August 6, 2012.]
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
=====================
A circular rainbow should not be confused with the glory, which is
much smaller in diameter and is created by different optical
processes. In the right circumstances, a glory and a (circular)
rainbow or fog bow can occur together. Another atmospheric phenomenon
that may be mistaken for a "circular rainbow" is the 22° halo, which
is caused by ice crystals rather than liquid water droplets, and is
located around the Sun (or Moon), not opposite it.
Supernumerary rainbows {{anchor|Supernumerary}}
=================================================
In certain circumstances, one or several narrow, faintly coloured
bands can be seen bordering the violet edge of a rainbow; i.e., inside
the primary bow or, much more rarely, outside the secondary. These
extra bands are called 'supernumerary rainbows' or 'supernumerary
bands'; together with the rainbow itself the phenomenon is also known
as a 'stacker rainbow'. The supernumerary bows are slightly detached
from the main bow, become successively fainter along with their
distance from it, and have pastel colours (consisting mainly of pink,
purple and green hues) rather than the usual spectrum pattern. The
effect becomes apparent when water droplets are involved that have a
diameter of about 1 mm or less; the smaller the droplets are, the
broader the supernumerary bands become, and the less saturated their
colours. Due to their origin in small droplets, supernumerary bands
tend to be particularly prominent in fogbows.
Supernumerary rainbows cannot be explained using classical geometric
optics. The alternating faint bands are caused by interference between
rays of light following slightly different paths with slightly varying
lengths within the raindrops. Some rays are in phase, reinforcing each
other through constructive interference, creating a bright band;
others are out of phase by up to half a wavelength, cancelling each
other out through destructive interference, and creating a gap. Given
the different angles of refraction for rays of different colours, the
patterns of interference are slightly different for rays of different
colours, so each bright band is differentiated in colour, creating a
miniature rainbow. Supernumerary rainbows are clearest when raindrops
are small and of uniform size. The very existence of supernumerary
rainbows was historically a first indication of the wave nature of
light, and the first explanation was provided by Thomas Young in
1804.See:
* Thomas Young (1804)
[
https://books.google.com/books?id=7AZGAAAAMAAJ&pg=PA1 "Bakerian
Lecture: Experiments and calculations relative to physical optics,"]
'Philosophical Transactions of the Royal Society of London' 94: 1-16;
see especially pp. 8-11.
* [
http://www.atoptics.co.uk/rainbows/supers.htm Atmospheric Optics:
Supernumerary Rainbows]
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". In the laboratory, it is possible to observe higher-order
rainbows by using extremely bright and well collimated light produced
by lasers. Up to the 200th-order rainbow was reported by Ng et al. in
1998 using a similar method but an argon ion laser beam.
Tertiary and quaternary rainbows should not be confused with "triple"
and "quadruple" rainbows--terms sometimes erroneously used to refer to
the (much more common) supernumerary bows and reflection rainbows.
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.See:
* [
http://www.atoptics.co.uk/droplets/fogbow.htm Atmospheric Optics:
Fogbow]
* James C. McConnel (1890)
[
https://books.google.com/books?id=fFAEAAAAYAAJ&pg=PA453 "The
theory of fog-bows,"] 'Philosophical Magazine', series 5, 29 (181):
453-461.
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.
Circumhorizontal and circumzenithal arcs
==========================================
Both arcs are brightly coloured ring segments centred on the zenith,
but in different positions in the sky: The circumzenithal arc is
notably curved and located high above the Sun (or Moon) with its
convex side pointing downwards (creating the impression of an "upside
down rainbow"); the circumhorizontal arc runs much closer to the
horizon, is more straight and located at a significant distance below
the Sun (or Moon). Both arcs have their red side pointing towards the
Sun and their violet part away from it, meaning the circumzenithal arc
is red on the bottom, while the circumhorizontal arc is red on top.
The circumhorizontal arc is sometimes referred to by the misnomer
"fire rainbow". In order to view it, the Sun or Moon must be at least
58° above the horizon, making it a rare occurrence at higher
latitudes. The circumzenithal arc, visible only at a solar or lunar
elevation of less than 32°, is much more common, but often missed
since it occurs almost directly overhead.
Extraterrestrial rainbows
===========================
It has been suggested that rainbows might exist on Saturn's moon
Titan, as it has a wet surface and humid clouds. The radius of a Titan
rainbow would be about 49° instead of 42°, because the fluid in that
cold environment is methane instead of water. Although visible
rainbows may be rare due to Titan's hazy skies, infrared rainbows may
be more common, but an observer would need infrared night vision
goggles to see them.
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 does not perfectly align with the ordinary rainbow, if seen at the
same spot. Tiny plastic or glass marbles may be used in road marking
as a reflectors to enhance its visibility by drivers at night. Due to
a much higher refractive index, rainbows observed on such marbles have
a noticeably smaller radius. One can easily reproduce such phenomena
by sprinkling liquids of different refractive indices in the air, as
illustrated in the photo.
The displacement of the rainbow due to different refractive indices
can be pushed to a peculiar limit. For a material with a refractive
index larger than 2, there is no angle fulfilling the requirements for
the first order rainbow. For example, the index of refraction of
diamond is about 2.4, so diamond spheres would produce rainbows
starting from the second order, omitting the first order. In general,
as the refractive index exceeds a number , where is a natural number,
the critical incidence angle for times internally reflected rays
escapes the domain . This results in a rainbow of the -th order
shrinking to the antisolar point and vanishing.
Scientific history
======================================================================
The classical Greek scholar Aristotle (384-322 BC) was first to devote
serious attention to the rainbow. According to Raymond L. Lee and
Alistair B. Fraser, "Despite its many flaws and its appeal to
Pythagorean numerology, Aristotle's qualitative explanation showed an
inventiveness and relative consistency that was unmatched for
centuries. After Aristotle's death, much rainbow theory consisted of
reaction to his work, although not all of this was uncritical."
In Book I of 'Naturales Quaestiones' (), the Roman philosopher Seneca
the Younger discusses various theories of the formation of rainbows
extensively, including those of Aristotle. He notices that rainbows
appear always opposite to the Sun, that they appear in water sprayed
by a rower, in the water spat by a fuller on clothes stretched on pegs
or by water sprayed through a small hole in a burst pipe. He even
speaks of rainbows produced by small rods (virgulae) of glass,
anticipating Newton's experiences with prisms. He takes into account
two theories: one, that the rainbow is produced by the Sun reflecting
in each water drop, the other, that it is produced by the Sun
reflected in a cloud shaped like a concave mirror; he favours the
latter. He also discusses other phenomena related to rainbows: the
mysterious "virgae" (rods), halos and parhelia.
According to Hüseyin Gazi Topdemir, the Arab physicist and polymath
Ibn al-Haytham (965-1039 AD) attempted to provide a scientific
explanation for the rainbow phenomenon. In his 'Maqala fi al-Hala wa
Qaws Quzah' ('On the Rainbow and Halo'), al-Haytham "explained the
formation of rainbow as an image, which forms at a concave mirror. If
the rays of light coming from a farther light source reflect to any
point on axis of the concave mirror, they form concentric circles in
that point. When it is supposed that the sun as a farther light
source, the eye of viewer as a point on the axis of mirror and a cloud
as a reflecting surface, then it can be observed the concentric
circles are forming on the axis." He was not able to verify this
because his theory that "light from the sun is reflected by a cloud
before reaching the eye" did not allow for a possible experimental
verification. This explanation was 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'.
In Song dynasty China (960-1279), a polymath scholar-official named
Shen Kuo (1031-1095) hypothesised--as a certain Sun Sikong (1015-1076)
did before him--that rainbows were formed by a phenomenon of sunlight
encountering droplets of rain in the air. Paul Dong writes that Shen's
explanation of the rainbow as a phenomenon of atmospheric refraction
"is basically in accord with modern scientific principles."
According to Nader El-Bizri, the Persian astronomer, Qutb al-Din
al-Shirazi (1236-1311), gave a fairly accurate explanation for the
rainbow phenomenon. This was elaborated on by his student, Kamāl
al-Dīn al-Fārisī (1267-1319), who gave a more mathematically
satisfactory explanation of the rainbow. He "proposed a model where
the ray of light from the sun was refracted twice by a water droplet,
one or more reflections occurring between the two refractions." An
experiment with a water-filled glass sphere was conducted and
al-Farisi showed the additional refractions due to the glass could be
ignored in his model. As he noted in his 'Kitab Tanqih al-Manazir'
('The Revision of the Optics'), al-Farisi used a large clear vessel of
glass in the shape of a sphere, which was filled with water, in order
to have an experimental large-scale model of a rain drop. He then
placed this model within a camera obscura that has a controlled
aperture for the introduction of light. He projected light unto the
sphere and ultimately deduced through several trials and detailed
observations of reflections and refractions of light that the colours
of the rainbow are phenomena of the decomposition of light.
In Europe, Ibn al-Haytham's 'Book of Optics' was translated into Latin
and studied by Robert Grosseteste. His work on light was continued by
Roger Bacon, who wrote in his 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 (Discours de la
Méthode),' further advanced this explanation. Knowing that the size of
raindrops did not appear to affect the observed rainbow, he
experimented with passing rays of light through a large glass sphere
filled with water. By measuring the angles that the rays emerged, he
concluded that the primary bow was caused by a single internal
reflection inside the raindrop and that a secondary bow could be
caused by two internal reflections. He supported this conclusion with
a derivation of the law of refraction (subsequently to, but
independently of, Snell) and correctly calculated the angles for both
bows. His explanation of the colours, however, was based on a
mechanical version of the traditional theory that colours were
produced by a modification of white light.
Isaac Newton demonstrated that white light was composed of the light
of all the colours of the rainbow, which a glass prism could separate
into the full spectrum of colours, rejecting the theory that the
colours were produced by a modification of white light. He also showed
that red light is refracted less than blue light, which led to the
first scientific explanation of the major features of the rainbow.
Newton's corpuscular theory of light was unable to explain
supernumerary rainbows, and a satisfactory explanation was not found
until Thomas Young realised that light behaves as a wave under certain
conditions, and can interfere with itself.
Young's work was refined in the 1820s by George Biddell Airy, who
explained the dependence of the strength of the colours of the rainbow
on the size of the water droplets.See:
*
* G. B. Airy (1849)
[
https://books.google.com/books?id=2vsIAAAAIAAJ&pg=PA595
"Supplement to a paper, "On the intensity of light in the
neighbourhood of a caustic," "] 'Transactions of the Cambridge
Philosophical Society' 8: 595-600. Modern physical descriptions of the
rainbow are based on Mie scattering, work published by Gustav Mie in
1908. Advances in computational methods and optical theory continue to
lead to a fuller understanding of rainbows. For example, Nussenzveig
provides a modern overview.
Experiments
======================================================================
Experiments on the rainbow phenomenon using artificial raindrops, i.e.
water-filled spherical flasks, go back at least to Theodoric of
Freiberg in the 14th century. Later, also Descartes studied the
phenomenon using a Florence flask. A flask experiment known as
Florence's rainbow is still often used today as an imposing and
intuitively accessible demonstration experiment of the rainbow
phenomenon. It consists in illuminating (with parallel white light) a
water-filled spherical flask through a hole in a screen. A rainbow
will then appear thrown back / projected on the screen, provided the
screen is large enough. Due to the finite wall thickness and the
macroscopic character of the artificial raindrop, several subtle
differences exist as compared to the natural phenomenon, including
slightly changed rainbow angles and a splitting of the rainbow orders.
A very similar experiment consists in using a cylindrical glass vessel
filled with water or a solid transparent cylinder and illuminated
either parallel to the circular base (i.e. light rays remaining at a
fixed height while they transit the cylinder) or under an angle to
the base. Under these latter conditions the rainbow angles change
relative to the natural phenomenon since the effective index of
refraction of water changes (Bravais' index of refraction for inclined
rays applies).
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 chapter 9, as part of the flood story of Noah, where it is a
sign of God's covenant to never destroy all life on Earth with a
global flood again. In Norse mythology, the rainbow bridge Bifröst
connects the world of men (Midgard) and the realm of the gods
(Asgard). Cuchavira was the god of the rainbow for the Muisca in
present-day Colombia and when the regular rains on the Bogotá savanna
were over the people thanked him, offering gold, snails and small
emeralds. Some forms of Tibetan Buddhism or Dzogchen 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, 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. In Albanian folk beliefs the rainbow is regarded as
the belt of the goddess Prende, and oral legend has it that anyone who
jumps over the rainbow changes their sex.
In heraldry, the rainbow proper consists of 4 bands of colour (argent,
gules, or, and vert) with the ends resting on clouds. Generalised
examples in coat of arms include those of the towns of Regen and
Pfreimd, both in Bavaria, Germany; of Bouffémont, France; and of the
69th Infantry Regiment (New York) of the United States Army National
Guard.
Rainbow flags have been used for centuries. It was a symbol of the
Cooperative movement in the German Peasants' War in the 16th century,
of peace in Italy, and of LGBT pride and LGBT social movements; the
rainbow flag as a symbol of LGBT pride and the June pride month since
it was designed by Gilbert Baker in 1978. In 1994, Archbishop Desmond
Tutu and President Nelson Mandela described newly democratic
post-apartheid South Africa as the rainbow nation. The rainbow has
also been used in technology product logos, including the Apple
computer logo. Many political alliances spanning multiple political
parties have called themselves a "Rainbow Coalition".
Pointing at rainbows has been considered a taboo in many cultures.
See also
======================================================================
* Atmospheric optics
* Circumzenithal arc
* Circumhorizontal arc
* Glory (optical phenomenon)
* Iridescent colours in soap bubbles
* Sun dog
* Fog bow
* Moonbow
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
======================================================================
*[
http://www.ams.org/publicoutreach/feature-column/fcarc-rainbows The
Mathematics of Rainbows], article from the American mathematical
society
* [
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=44.0
Interactive simulation of light refraction in a drop (java applet)]
*
[
https://web.archive.org/web/20110718165204/http://www.grad.ucl.ac.uk/comp/2007-2008/research/gallery/index.pht?entryID=183
Rainbow seen through infrared filter and through ultraviolet filter]
* [
http://www.atoptics.co.uk/bows.htm 'Atmospheric Optics' website by
Les Cowley] - Description of multiple types of bows, including: "bows
that cross, red bows, twinned bows, coloured fringes, dark bands,
spokes", etc.
*
* [
https://www.youtube.com/watch?v=BU1n0mtB1xs Creating Circular and
Double Rainbows!] - video explanation of basics, shown artificial
rainbow at night, second rainbow and circular one.
License
=========
All content on Gopherpedia comes from Wikipedia, and is licensed under CC-BY-SA
License URL:
http://creativecommons.org/licenses/by-sa/3.0/
Original Article:
http://en.wikipedia.org/wiki/Rainbow
