A
rainbow is an
optical and
meteorological phenomenon that causes a
spectrum of
light to appear in the sky when the Sun shines onto
droplets of moisture in the
Earth's
atmosphere. They take the form of a
multicoloured arc, with
red on the outer part of the
arch and
violet on the inner section of the
arch.
A rainbow spans a continuous spectrum
of colours; the discrete bands are an artefact of human
colour vision. The most commonly cited and
remembered sequence, in English, is
Newton's sevenfold red, orange, yellow, green,
blue,
indigo and violet (popularly memorized
by
mnemonics like Roy G. Biv).Rainbows can be caused by other forms of
water than rain, including mist, spray, and
dew.
Rainbows may also form in mist, such as that of a waterfall
Rainbow with a faint reflected rainbow
in the lake
Visibility
Rainbows may also form in the spray created by waves (called
spray bows).
Rainbows can be observed whenever there are water
drops in the air and
sunlight shining from behind a person at a low
altitude angle (on the
ground). The most spectacular rainbow displays happen when half of
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.
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 semi-circle of a rainbow in one frame,
as this would require an
angle of view
of 84°. For a
35 mm camera, a lens
with a focal length of 19 mm or less
wide-angle lens would be required. Now that
powerful 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 an
aeroplane, one has the
opportunity to see the whole circle of the rainbow, with the
plane's shadow in the centre. This phenomenon can be confused with
the
glory, but a glory is
usually much smaller, covering only 5°–20°.
At good visibility conditions (for example, a dark cloud behind the
rainbow), the second arc can be seen, with inverse order of
colours.At the background of the blue sky, the second arc is barely
visible.
Scientific explanation
The light is first
refracted as it enters
the surface of the raindrop,
reflected off the back of the drop, and
again refracted as it leaves the drop. The overall effect is that
the incoming light is reflected back over a wide range of
angles, with the most intense light at an angle of
40°–42°. The angle is independent of the size of the drop, but does
depend on its
refractive index.
Seawater has a higher refractive index than rain water, so the
radius of a 'rainbow' in sea spray is smaller than a true rainbow.
This is visible to the naked eye by a misalignment of these
bows.The amount by which light is refracted depends upon its
wavelength, and hence its colour. 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. You
may then think it is strange that the pattern of colours in a
rainbow has red on the outside of the arc and blue on the inside.
However, when we examine this issue more closely, we realise that
if the red light from one droplet is seen by an observer, then the
blue light from that droplet will not be seen because it must be on
a different path from the red light: a path which is not incident
with the observer's eyes. The blue light seen in this rainbow will
therefore come from a
different droplet, which must be
below that whose red light can be observed.
Contrary to popular belief, the light at the back of the raindrop
does not undergo
total
internal reflection, and some light does emerge from the back.
However, light coming out the back of the raindrop does not create
a rainbow between the observer and the sun because spectra emitted
from the back of the raindrop do not have a maximum of intensity,
as the other visible rainbows do, and thus the colours blend
together rather than forming a rainbow.
Light rays enter a raindrop from one direction (typically a
straight line from the Sun), reflect off the back of the raindrop,
and fan out as they leave the raindrop.
The light leaving the rainbow is spread over a wide angle,
with a maximum intensity at 40.89°–42°.
|
White light separates into different colours on entering the
raindrop because red light is refracted by a lesser angle than blue
light.
On leaving the raindrop, the red rays have turned through a
smaller angle than the blue rays, producing a rainbow.
|
A rainbow does not actually exist at a particular location in the
sky. Its apparent position depends on the observer's location and
the position of 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 position of a rainbow in the sky is
always in the opposite direction of the Sun with respect to the
observer, and the interior is always slightly brighter than the
exterior. The bow is centred on the shadow of the observer's head,
or more exactly at the
antisolar
point (which is below the
horizon during
the daytime), appearing at an angle of 40°–42° to the line between
the observer's head and its shadow. As a result, if the Sun is
higher than 42°, then the rainbow is below the horizon and cannot
be seen as there are not usually sufficient raindrops between the
horizon (that is: eye height) and the ground, to contribute.
Exceptions occur when the observer is high above the ground, for
example in an aeroplane (see above), on top of a mountain, or above
a waterfall.
Variations
Frequently, a dim secondary rainbow is seen outside the primary
bow. Secondary rainbows are caused by a double reflection of
sunlight inside the raindrops, and appear at an angle of 50°–53°.
As a result of the second reflection, the colours of a secondary
rainbow are inverted compared to the primary bow, with blue on the
outside and red on the inside. 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.
A third, or tertiary, rainbow can be seen on rare occasions, and a
few observers have reported seeing quadruple rainbows in which a
dim outermost arc had a rippling and pulsating appearance. These
rainbows would appear on the same side of the sky as the Sun,
making them hard to spot. One type of tertiary rainbow carries with
it the appearance of a secondary rainbow immediately outside the
primary bow. The closely spaced outer bow has been observed to form
dynamically at the same time that the outermost (tertiary) rainbow
disappears. During this change, the two remaining rainbows have
been observed to merge into a band of white light with a blue inner
and red outer band. This particular form of doubled rainbow is not
like the classic double rainbow due to both spacing of the two bows
and that the two bows share identical normal colour positioning
before merging. With both bows, the inner colour is blue and the
outer colour is red.
Higher-order rainbows were described by Felix Billet (1808-1882)
who depicted angular positions up to the 19
th-order
rainbow. A pattern he called “rose”.In the laboratory, it is
possible to observe higher-order rainbows by using extremely bright
and well
collimated light produced by
lasers. A sixth-order rainbow was first
observed by K. Sassan in 1979 using a
HeNe
laser beam and a pendant water drop. Up to the
200
th-order rainbow was reported by Ng et al. in 1998
using a similar method but an argon ion laser beam.
Supernumerary rainbow
A
supernumerary rainbow is an infrequent
phenomenon, consisting of several faint rainbows on the inner side
of the primary rainbow, and very rarely also outside the secondary
rainbow. Supernumerary rainbows are slightly detached and have
pastel colour bands that do not fit the usual pattern.
It is not possible to explain their existence using classical
geometric
optics. The alternating faint
rainbows 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
similar 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.
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 will appear as a mirror image in
the water surface below the horizon, if the surface is quiet (see
photo above). 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.
Where sunlight reflects off a body of water before reaching the
raindrops (see
diagram), it may produce a
reflection
rainbow (see photo at the right), if the water body is
large, and 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. Due to the combination of requirements, a
reflection rainbow is rarely visible.
Six (or even eight) bows may be distinguished if the reflection of
the reflection bow, and the secondary bow with its reflections
happen to appear as well.
Circumhorizontal arc
The
circumhorizontal arc is
sometimes referred to by the misnomer 'fire rainbow'. As it
originates in ice crystals it is not a rainbow but a
halo.
Rainbows on Titan
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. A visitor might need
infrared goggles to see the rainbow, as Titan's
atmosphere is more transparent for those wavelengths.
Scientific history
The
Persian physicist and
polymath,
Ibn
al-Haytham (Alhazen; 965-1039), attempted to provide a
scientific explanation for the rainbow phenomenon. In his
Maqala fi al-Hala wa Qaws Quzah (
On the Rainbow and
Halo), he "explained the formation of rainbow as an image,
which forms at a concave mirror. If the rays of light coming from a
farther light source reflect to any point on axis of the concave
mirror, they form concentric circles in that point. When it is
supposed that the sun as a farther light source, the eye of viewer
as a point on the axis of mirror and a cloud as a reflecting
surface, then it can be observed the concentric circles are forming
on the axis." He was not able to verify this because his theory
that "light from the sun is reflected by a cloud before reaching
the eye" did not allow for a possible
experimental verification. This explanation was
later repeated by
Averroes, and, though
incorrect, provided the groundwork for the correct explanations
later given by
Kamāl al-Dīn
al-Fārisī (1267-ca.1319/1320) and
Theodoric of Freiberg.
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.
In
Song Dynasty China (960–1279), a
polymathic
scholar-official named
Shen Kuo (1031–1095) hypothesized—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."
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 (1260–1320), 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." He verified this through extensive experimentation
using a transparent sphere filled with water and a
camera obscura. 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 deducted 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. His research had resonances with the
studies of his contemporary
Theodoric of Freiberg (without any
contacts between them; even though they both relied on Ibn
al-Haytham's legacy), and later with the experiments of
Descartes and
Newton
in dioptrics (for instance, Newton conducted a similar experiment
at Trinity College, though using a prism rather than a
sphere).
In Europe, Ibn al-Haytham's
Book of
Optics was
translated into Latin
and studied by
Robert
Grosseteste. His work on light was continued by
Roger Bacon, who wrote in his
Opus Majus of 1268 about experiments with
light shining through crystals and water droplets showing the
colours of the rainbow.
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.
René Descartes' sketch of how primary
and secondary rainbows are formed
Descartes 1637 treatise,
Discourse on Method,
further advanced this explanation. Knowing that the size of
raindrops did not appear to affect the observed rainbow, he
experimented with passing rays of light through a large glass
sphere filled with water. By measuring the angles that the rays
emerged, he concluded that the primary bow was caused by a single
internal reflection inside the raindrop and that a secondary bow
could be caused by two internal reflections. He supported this
conclusion with a derivation of the law of
refraction (subsequently, 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 gets refracted less than blue light, which
led to the first scientific explanation of the major features of
the rainbow. Newton's corpuscular theory of light was unable to
explain supernumerary rainbows, and a satisfactory explanation was
not found until
Thomas
Young realised that light behaves as a wave under certain
conditions, and can
interfere with
itself.
Young's work was refined in the 1820s by
George Biddell Airy, who explained the
dependence of the strength of the colours of the rainbow on the
size of the water droplets. Modern physical descriptions of the
rainbow are based on
Mie scattering,
work published by
Gustav Mie in 1908.
Advances in computational methods and optical theory continue to
lead to a fuller understanding of rainbows. For example,
Nussenzveig provides a modern overview.
Culture
Religion and mythology
The end of a rainbow.
The rainbow has a place in legend owing to its beauty and the
historical difficulty in explaining the phenomenon.
In
Greek mythology, the rainbow was
considered to be a path made by a messenger (
Iris) between Earth and Heaven. In
Chinese mythology, the rainbow was a slit
in the sky sealed by Goddess
Nüwa using
stones of five different colours. In
Hindu mythology, the rainbow is called
"
Indradhanush", meaning the
bow (
Sanskrit &
Hindi: dhanush is bow) of
Indra, the God of
lightning,
thunder and
rain.
Another Indian mythology says rainbow is the bow of Kama, the God
of love. It is called Kamanabillu in
Kannada, billu meaning bow. In
Norse Mythology, a rainbow called the
Bifröst Bridge connects the realms of
Ásgard and
Midgard, homes of the gods and humans, respectively.
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 impossible to reach, because the rainbow is
an optical effect which depends on the location of the viewer. When
walking towards the end of a rainbow, it will move further
away.
After
Noah's Flood, the
Bible relates that the rainbow gained meaning as the
sign of God's promise that terrestrial life would never again be
destroyed by flood (Genesis 9.13-17):
I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth.
And it shall come to pass, when I bring a cloud over the earth, that the bow shall be seen in the cloud:
And I will remember my covenant, which is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh.
And the bow shall be in the cloud; and I will look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth.
And God said unto Noah, This is the token of the covenant, which I have established between me and all flesh that is upon the earth.
Another ancient portrayal of the rainbow is given in the
Epic of Gilgamesh: the rainbow is the
"jewelled necklace of the Great Mother
Ishtar" that she lifts into the sky as a promise that
she "will never forget these days of the great flood" that
destroyed her children. (
The Epic
of Gilgamesh, Tablet Eleven)
Then Ishtar arrived. She lifted up the necklace of
great jewels that her father, Anu, had created to please her and
said, "Heavenly gods, as surely as this jewelled necklace hangs
upon my neck, I will never forget these days of the great flood.
Let all of the gods except Enlil come to the offering. Enlil may
not come, for without reason he brought forth the flood that
destroyed my people."
In the Dreamtime of Australian Aboriginal
mythology, the rainbow snake is
the deity governing water.
In New Age and Hindu philosophy, the seven colours of the
rainbow represent the seven chakras, from the
first chakra (red) to the seventh chakra (violet).
Art
Rainbows are generally described as very colourful and peaceful.
The rainbow occurs often in paintings. Frequently these have a
symbolic or programmatic significance (for example, Albrecht Dürer's Melancholia I). In particular, the rainbow
appears regularly in religious art (for example, Joseph Anton Koch's Noah's
Thanksoffering). Romantic landscape painters such as Turner and Constable were more concerned with recording
fleeting effects of light (for example, Constable's Salisbury Cathedral from
the Meadows). Other notable examples appear in work by Hans Memling, Caspar David Friedrich, and Peter Paul Rubens.
Literature
The rainbow inspires metaphor and simile. Virginia Woolf in To the Lighthouse highlights the
transience of life and Man's mortality through Mrs Ramsey's
thought,
- "it was all as ephemeral as a rainbow"
Wordsworth's 1802 poem "My Heart Leaps Up When I
Behold The Rainbow" begins:
- My heart leaps up when I behold
- :A rainbow in the sky:
- So was it when my life began;
- So is it now I am a man;
- So be it when I shall grow old,
- :Or let me die!…
The Newtonian deconstruction of the
rainbow is said to have provoked John
Keats to lament in his 1820 poem "Lamia":
- Do not all charms fly
- At the mere touch of cold philosophy?
- There was an awful rainbow once in heaven:
- We know her woof, her texture; she is given
- In the dull catalogue of common things.
- Philosophy will clip an Angel's wings,
- Conquer all mysteries by rule and line,
- Empty the haunted air, and gnomed mine –
- Unweave a rainbow
In contrast to this is Richard
Dawkins; talking about his book Unweaving the Rainbow: Science,
Delusion and the Appetite for Wonder:
- "My title is from Keats, who believed that
Newton had destroyed all the poetry of
the rainbow by reducing it to the prismatic colours. Keats could
hardly have been more wrong, and my aim is to guide all who are
tempted by a similar view, towards the opposite conclusion. Science
is, or ought to be, the inspiration for great poetry."
Music
- In the song "Over the Rainbow"
from The Wizard of
Oz, lead character Dorothy
Gale fantasizes about a place over the rainbow, where the world
is in peace and harmony.
- In "Rainbow Connection", a
song known for being sung by Kermit the
Frog, the idea of a rainbow is seen as something to wish on, as
it is popularly seen as a vision, or symbol of hope.
- In the 1995 hit song "Waterfalls" by TLC (written by the late Lisa "Left Eye" Lopes),
it is mentioned: "I seen a rainbow yesterday, but too many storms
have come, and gone, leaving a trace of not one God given
ray".
- In the "End of the Rainbow"
by September, the singer sings
about the rainbow, and how she will be at the end of the rainbow
and her ex could see her there when he reaches the end of the
rainbow.
- End of the rainbow is an
award winning stage play with music (or musical drama) by Peter Quilter.
- See also the group Rainbow and
the song "Rainbow Demon" by Uriah
Heep.
- Radiohead's seventh studio album
In Rainbows is a reference to rainbows,
particularly the sense of colour and the idea that rainbows signify
not only good, but bad things.
Flags
Historically, a rainbow flag was used in the German Peasants' War in the 16th century as a sign of
a new era, of hope and of social change. Rainbow flags have
also been used as a symbol of the Cooperative movement; as a symbol of peace,
especially in Italy; to represent the Tawantin Suyu, or Inca
territory, mainly in Peru
and Bolivia
; by some
Druze communities in the Middle east; and by the Jewish
Autonomous Oblast
.
A rainbow flag has been
in use as a symbol of gay pride and
LGBT social movements since
the 1970s. The colours reflect the diversity of the LGBT community. It was originally
designed by San
Francisco
artist
Gilbert Baker in
1978.
Distinct colours
Newton originally (1672) named only five primary colours:
red, yellow, green, blue and violet. Only later did he introduce
orange and indigo, giving seven colours by analogy to the number of
notes in a musical scale. The division in distinct colours is an
arbitrary convention. It is related to the linguistic question
whether the colour terms are mainly culturally determined, and
different between people; or biologically determined, and universal
for all people (the colour
debate). From a physics point of view, the rainbow spans a
continuous spectrum of colours -- there are no "bands."
Red = , Orange = , Yellow = , Green = , Blue = , Indigo = , Violet = .
Effects to be distinguished from rainbow
Notes
- Cowley, Les. "Zero
order glow" Atmospheric Optics.
- K. Sassen, J. Opt. Soc. Am. 69 (1979) 1083.
- P. H. Ng, M. Y. Tse, and W. K. Lee, J. Opt. Soc. Am. B
15 (1998) 2782
- Carl Benjamin Boyer (1954), "Robert
Grosseteste on the Rainbow", Osiris 11:
247-258 [248]
- Sivin, Nathan (1995). Science in Ancient China: Researches and
Reflections. Brookfield, Vermont: VARIORUM, Ashgate Publishing.
III, Page 24.
- Dong, Paul (2000), China's Major Mysteries: Paranormal
Phenomena and the Unexplained in the People's Republic, p. 72,
San Francisco: China Books and Periodicals, Inc., ISBN
0835126765
- Nader El-Bizri, "Ibn al-Haytham", in Medieval Science,
Technology, and Medicine: An Encyclopedia, eds. Thomas F.
Glick, Steven J. Livesey, and Faith Wallis (New York — London:
Routledge, 2005), pp. 237-240.
- Nader El-Bizri, "Optics", in Medieval Islamic Civilization:
An Encyclopedia, ed. Josef W. Meri (New York – London:
Routledge, 2005), Vol. II, pp. 578-580
- Nader El-Bizri, "Al-Farisi, Kamal al-Din," in The
Biographical Encyclopaedia of Islamic Philosophy, ed. Oliver
Leaman (London — New York: Thoemmes Continuum, 2006), Vol. I, pp.
131-135
- Nader El-Bizri, "Ibn al-Haytham, al-Hasan", in The
Biographical Encyclopaedia of Islamic Philosophy, ed. Oliver
Leaman (London — New York: Thoemmes Continuum, 2006), Vol. I, pp.
248-255.
- Nussenzveig, H. Moyses, "The Theory of the Rainbow,"
Scientific American Vol.236, No.4 (1977), 116.
- Holy Bible: (2004).Intellectual
Reserve,inc.
- http://flagspot.net/flags/xi.html
- http://www1.umn.edu/ships/updates/newton1.htm
References
- Graham, Lanier F. (editor) The Rainbow Book Berkeley,
California: Shambhala Publications and The Fine Arts Museums of San
Francisco (1976) (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.)
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