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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.
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Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind at a low altitude angle. 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.[1] 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 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.
The light is first refracted entering 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.[2] 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.[3]
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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.
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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 19th-order rainbow. A pattern he called “rose”.[4] 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.[5] Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam.[6]
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.
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 simultaneously.[7]
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.[8]
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.[9]
The Islamic 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."[10] 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.[11] This explanation was later repeated by Averroes,[10] 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.[12]
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."[13] This explanation, however, was also incorrect.[10]
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.[14] Paul Dong writes that Shen's explanation of the rainbow as a phenomenon of atmospheric refraction "is basically in accord with modern scientific principles."[15]
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.[11] 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).[16][17][18][19]
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.[20] 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".[21] He explained the secondary rainbow through a similar analysis involving two refractions and two reflections.
Descartes 1637 treatise, Discourse on Method, further advanced this explanation. Knowing that the size of raindrops did not appear to affect the observed rainbow, he experimented with passing rays of light through a large glass sphere filled with water. By measuring the angles that the rays emerged, he concluded that the primary bow was caused by a single internal reflection inside the raindrop and that a secondary bow could be caused by two internal reflections. He supported this conclusion with a derivation of the law of refraction (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.[22][23]
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.[24] 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.[25]
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. Likewise, in mythology of Arabian Peninsula, rainbow, called Qaus Quzaħ in Arabic, is the war bow of the god Quzaħ.
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)[26]:
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).
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.
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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,
Wordsworth's 1802 poem "My Heart Leaps Up When I Behold The Rainbow" begins:
The Newtonian deconstruction of the rainbow is said to have provoked John Keats to lament in his 1820 poem "Lamia":
In contrast to this is Richard Dawkins; talking about his book Unweaving the Rainbow: Science, Delusion and the Appetite for Wonder:
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;[27] by some Druze communities in the Middle east; and by the Jewish Autonomous Oblast.
A Rainbow flag has been used to represent the International Order of Rainbow for Girls since the early 1920's.
A rainbow flag has been in use as a symbol of gay pride and LGBT social movements since the 1970s.[28][29]
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[30]. 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 = .
Rainbows — Phenomena of Light and Mind...
RAINBOW, formerly known as the iris, the coloured rings seen in the heavens when the light from the sun or moon shines on falling rain; on a smaller scale they may be observed when sunshine falls on the spray of a waterfall or fountain. The bows assume the form of concentric circular arcs, having their common centre on the line joining the eye of the observer to the sun. Generally only one bow is clearly seen; this is known as the primary rainbow; it has an angular radius of about 410, and exhibits a fine display of the colours of the spectrum, being red on the outside and violet on the inside. Sometimes an outer bow, the secondary rainbow, is observed; this is much fainter than the primary bow, and it exhibits the same play of colours, with the important distinction that the order is reversed, the red being inside and the violet outside. Its angular radius is about J7°. It is also to be noticed that the space between the two bows is considerably darker than the rest of the sky. In addition to these prominent features, there are sometimes to be seen a number of coloured bands, situated at or near the summits of the bows, close to the inner edge of the primary and the outer edge of the secondary bow; these are known as the spurious, supernumerary or complementary rainbows. The formation of the rainbow in the heavens after or during a shower must have attracted the attention of man in remote antiquity. The earliest references are to be found in the various accounts of the Deluge. In the Biblical narrative (Gen. ix. 12-17) the bow is introduced as a sign of the covenant between God and man, a figure without a parallel in the other accounts. Among the Greeks and Romans various speculations as to the cause of the how were indulged in; Aristotle, in his Meteors, erroneously ascribes it to the reflection of the sun's rays by the rain; Seneca adopted the same view. The introduction of the idea that the phenomenon was caused by refraction is to be assigned to Vitellio. The same conception was utilized by Theodoric of Vriberg, a Dominican, who wrote at some time between 1304 and 1311 a tract entitled De radialibus impressionibus, in which he showed how the primary bow is formed by two refractions and one internal reflection; i.e. the light enters the drop and is refracted; the refracted ray is then reflected at the opposite surface of the drop, and leaves the drop at the same side at which it enters, being again refracted. It is difficult to determine the influence which the writings of Theodoric had on his successors; his works were apparently unknown until they were discovered by G. B. Venturi at Basel, partly in the city library and partly in the library of the Dominican. monastery. A full account, together with other early contributions to the science of light, is given in Venturi's Commentari sopra la storia de la Teoria del Ottica (Bologna, 1814). John Fleischer (sometimes incorrectly named Fletcher), of Breslau, propounded the same view in a pamphlet, De iridibus doctrina Aristotelis et Vitellonis (1574) the same explanation was given by Franciscus Maurolycus in his Photismi de lumine et umbra (1575) The most valuable of all the earlier contributions to the scientific explanation of rainbows is undoubtedly a treatise by Marco Antonio de Dominis (1566-1624), archbishop of Spalatro. This work, De radiis visas et lucis in vitris perspectivis et iride, published at Venice in 1611 by J. Bartolus, although written some twenty years previously, contains a chapter entitled "Vera iridis tota generatis explicatur," in which it is shown how the primary bow is formed by two refractions and one reflection, and the secondary bow by two refractions and two reflections. Descartes strengthened these views, both by experiments and geometrical investigations, in his Meteors (Leiden, 1637). He employed the law of refraction (discovered by W. Snellius) to calculate the radii of the bows, and his theoretical angles were in agreement with those observed. His methods, however, were not free from tentative assumptions, and were considerably improved by Edmund Halley (Phil. Trans., 1700, 714). Descartes, however, could advance no satisfactory explanation of the chromatic displays; this was effected by Sir Isaac Newton, who, having explained how white light is composed of rays possessing all degrees of refrangibility, was enabled to demonstrate that the order of the colours was in perfect accord with the requirements of theory (see Newton's Opticks, book i. part 2, prop. 9).
The geometrical theory, which formed the basis of the investigations of Descartes and Newton, afforded no explanation of the supernumerary bows, and about a century elapsed before an explanation was forthcoming. This was given by Thomas Young, who, in the Bakerian lecture delivered before the Royal Society on the 24th of November 1803, applied his principle of the interference of light to this phenomenon. His not wholly satisfactory explanation was mathematically examined in 1835 by Richard Potter (Camb. Phil. Trans., 1838, 6, 141), who, while improving the theory, left a more complete solution to be made in 1838 by Sir George Biddell Airy (Camb. Phil. Trans., 1838, 6, 379).
The geometrical theory first requires a consideration of the path of a ray of light falling upon a transparent sphere. Of the total amount of light falling on such a sphere, part is reflected or scattered at the incident surface, so rendering the drop visible, while a part will enter the drop. Confining our attention to a ray entering in a principal plane, we will determine its deviation, i.e. the angle between its directions of incidence and emergence, after one, two, three or more internal reflections. Let EA be a ray incident at an angle i (fig. I); let AD be the refracted ray, and r the angle of refraction. Then the deviation experienced by the ray at A is i - r. If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle ADB equals 2r, i.e. the deviation of the ray at D is 7r-2r. At B, where the ray leaves the drop, the deviation is the same as at A, viz. i - r. The total deviation of the ray is consequently given by D =2(i - r) +7r - 2r.
Similarly it may be shown that each internal reflection introduces a supplementary deviation of 7r - 2r; hence, if the ray be reflected n times, the total deviation will be D =2(i - r) +n (7r - 2r) .
The deviation is thus seen to vary with the angle of incidence; and by considering a set of parallel rays passing through the same principal plane of the sphere and incident at all angles, it can be readily shown that more rays will pass in the neighbourhood of the position of minimum deviation than in any other position (see Refraction). The drop will consequently be more intensely illuminated when viewed along these directions of minimum deviation, and since it is these rays with which we are primarily concerned, we shall proceed to the determination of these directions.
Since the angles of incidence and refraction are connected by the relation sin i=µ sin r (Snell's Law), µ being the index of refraction of the medium, then the problem may be stated as follows: to determine the value of the angle i which makes D = 2 (i - r) +n (7r - 2r) a maximum or minimum, in which i and r are connected by the relation sin i =µ sin r, µ being a constant. By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or analytically that this is a minimum. For the angle i to be real, cos i must be a fraction, that is n 2 +2n>µ 2 - I, or (n+I)2>µ2. Since the value of µ for water is about, it follows that n must be at least unity for a rainbow to be formed; there is obviously no theoretical limit to the value of n, and hence rainbows of higher orders are possible.
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n |
Red. |
Violet. |
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I |
7r - |
42° I |
7r - |
4 |
° 22 |
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2 |
27r - |
12 |
° 2 |
27r - |
12 |
° 48 |
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3 |
37r- |
231 |
° 4 |
37r- |
22 |
° 08 |
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- 4zr-31 |
° 07 |
47r- |
31 |
° 07 |
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So far we have only considered rays of homogeneous light, and it remains to investigate how lights of varying refrangibilities will be transmitted. It can be shown. by the methods of the differential calculus or geometrically, that the deviation increases with the refractive index, the angle of incidence remaining constant. Taking the refractive index of water for the red rays as 0;, and for the violet rays as 1 r, we can calculate the following values for the minimum deviations corresponding to certain assigned values of n. To this point we have only considered rays passing through a principal section of the drop; in nature, however, the rays impinge at every point of the surface facing the sun. It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table. Thus, rays suffering one internal reflection will all lie within a cone of about 42°; in this direction the illumination will be most intense; within the cone the illumination will be fainter, while, without it, no light will be transmitted to the eye.
Fig. 2 represents sections of the drop and the cones containing the minimum deviation rays after I, 2, 3 and 4 reflections; the order of the colours is shown by the letters R (red) and V (violet). It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays. The observer will, therefore, see a coloured band, about 2° in width, and coloured violet inside and red outside. Within the band, the illumination FIG. 2 will be faint; outside the band there will be perceptible darkening until the second bow comes into view. Similarly, drops transmitting rays after two internal reflections will be situated on covertical and coaxial cones, of which the semi-vertical angles are 51° for the red rays and 54° for the violet. Outside the cone of 54° there will be faint illumination; within it, no secondary rays will be transmitted to the eye. We thus see that the order of colours in the secondary bow is the reverse of that in the primary; the secondary is half as broad again (3°), and is much fainter, owing to the longer path of the ray in the drop, and the increased dispersion.
Similarly, the third, fourth and higher orders of bows may be investigated. The third and fourth bows are situated between the observer and the sun, and hence, to be viewed, the observer must face the sun. But the illumination of the bow is so weakened by the repeated reflections, and the light of the sun is generally so bright, that these bows are rarely, if ever, observed except in artificial rainbows. The same remarks apply to the fifth bow, which differs from the third and fourth in being situated in the same part of the sky as the primary and secondary bows, being just above the secondary.
The most conspicuous colour band of the principal bows is the red; the other colours shading off into one another, generally with considerable blurring. This is due to the superposition of a great number. of spectra, for the sun has an appreciable apparent diameter, and each point on its surface gives rise to an individual spectrum. This overlapping may become so pronounced as to produce a rainbow in which colour is practically absent; this is particularly so when a thin cloud intervenes between the sun and the rain, which has the effect of increasing the apparent diameter of the sun to as much as 2° or 3°. This phenomenon is known as the "white rainbow" or "Ulloa's Ring or Circle," after Antonio de Ulloa.
We have now to consider the so-called spurious bows which are sometimes seen at the inner edge of the primary and at the outer edge of the secondary bow. The geometrical theory can afford no explanation of these coloured bands, and it has been shown that the complete phenomenon of the rainbow is to be sought for in the conceptions of the wave theory of light. This was first suggested by Thomas Young, who showed that the rays producing the bows consisted of two systems, which, although emerging in parallel directions, traversed different paths in the drop. Destructive interference between these superposed rays will therefore occur, and, instead of a continuous maximum illumination in the direction of minimum deviation, we should expect to find alternations of brightness and darkness. The later investigations of Richard Potter and especially of Sir George Biddell Airy have proved the correctness of Young's idea. The mathematical discussion of Airy showed that the primary rainbow is not situated directly on the line of minimum deviation, but at a slightly greater value; this means that the true angular radius of the bow is a little less than that derived from the geometrical theory. In the same way, he showed that the secondary bow has a greater radius than that previously assigned to it. The spurious bows he showed to consist of a series of dark and bright bands, whose distances from the principal bows vary with the diameters of the raindrops. The smaller the drops, the greater the distance; hence it is that the spurious bows are generally only observed near the summits of the bows, where the drops are smaller than at any lower altitude. In Airy's investigation, and in the extensions by Boitel, J. Larmor, E. Mascart and L. Lorentz, the source of light was regarded as a point. In nature, however, this is not realized, for the sun has an appreciable diameter. Calculations taking this into account have been made by J. Pernter (Neues fiber den Regenbogen, Vienna, 1888) and by K. Aichi and T. Tanakadate (Jour. College of Science, Tokyo, 1906, vol. xxi. art. 3).
Experimental confirmation of Airy's theoretical results was afforded in 1842 by William Hallows Miller (Camb. Phil. Trans. vii. 277). A horizontal pencil of sunlight was admitted by a vertical slit, and then allowed to fall on a column of water supplied by a jet of about th of an inch in diameter. Primary, secondary and spurious bows were formed, and their radii measured; a comparison of these observations exhibited agreement with Airy's analytical values. Pulfrich (Wied. Ann., 1888, 33, 194) obtained similar results by using cylindrical glass rods in place of the column of water.
In accordance with a general consequence of reflection and refraction, it is readily seen that the light of the rainbow is partially polarized, a fact first observed in 1811 by Jean Baptiste Biot (see Polarization).
FIG. I.
Lunar rainbows. The moon can produce rainbows in the same manner as the sun. The colours are much fainter, and according to Aristotle, who claims to be the first observer of this phenomenon, the lunar bows are only seen when the moon is full.
Marine rainbow is the name given to the chromatic displays formed by the sun's rays falling on the spray drawn up by the wind playing on the surface of an agitated sea.
Intersecting rainbows are sometimes observed. They are formed by parallel rays of light emanating from two sources, as, for example, the sun and its image in a sheet of water, which is situated between the observer and the sun. In this case the second bow is much fainter, and has its centre as much above the horizon as that of the direct system is below it.
. - For the history of the theory of the rainbow, see G. B. Venturi, Commentari sopra la stories de la teoria del Ottica (Bologna, 1814); F. Rosenberger, Geschichte der Physik (1882-90). The geometrical and physical theory is treated in T. Preston's Theory of Light; E. Mascart's Traite d'optique (1899-1903); and most completely by J. Pernter in various contributions to scientific journals and in his Meteorologische Optik (1905-9).
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William Joseph Rainbow (1856-1919).
caused by the reflection and refraction of the rays of the sun
shining on falling rain. It was
appointed as a witness of the divine faithfulness (Gen 9:12-17). It existed indeed
before, but it was then constituted as a sign of the covenant.
Others, however (as Delitzsch, Commentary on Pentateuch), think that it "appeared then
for the first time in the vault and clouds of heaven." It is argued by those holding this
opinion that the atmosphere was differently constituted before the
Flood. It is referred to three other times in Scripture (Ezek 1:27, 28; Rev 4:1-3; 10:1).
what mentions this? (please help by turning references to this page into wiki links)
[[File:|thumb|A rainbow arches over the gardens at the Canada pavilion at Epcot in Walt Disney World, Lake Buena Vista, Florida, United States.]]
A rainbow is an arc of colour in the sky that you can see when the sun shines through falling rain. The pattern of colors starts with red on the outside and changes through orange, yellow, green, blue, indigo to violet on the inside.
A rainbow is actually round. On the ground, the bottom part is hidden, but in the sky, like from the view of a flying airplane, it can be seen as a round shape. Rainbows are popular symbols that can mean peace and harmony. Rainbows are also recognizable symbols of gay pride.
The rainbow effect can be seen when:
The rainbow displays with the deepest effect in our minds take place when:
Another common place to see the rainbow effect is near waterfalls. Parts of rainbows can be seen some of the time:
An unnatural rainbow effect can also be made putting drops of water into the air on a sunny day.
Note: The spectrum colors can only be approximated on a computer screen but the colors shown below are a close approximation of the spectrum colors of the rainbow.
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bjn:Téjakoi:Енӧшка
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