A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the sun shines on droplets of moisture in the earth's atmosphere. It takes the form of a multicolored arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.

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 while 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 colors reversed, red facing toward the other one, in both rainbows. This second rainbow is caused by light reflecting twice inside water droplets.

The rainbow is not located at a specific distance, but comes from any water droplets viewed from a certain angle relative to the Sun's rays. Thus, a rainbow is not a physical object, and cannot be physically approached. Indeed, it is impossible for an observer to manoeuvre to see any rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the Sun. Even if an observer sees another observer who seems "under" or "at the end" of a rainbow, the second observer will see a different rainbow further off-yet, at the same angle as seen by the first observer.

A rainbow spans a continuous spectrum of colors. Any distinct bands perceived are an artifact of human color vision, and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side. For colors seen by a normal human eye, the most commonly cited and remembered sequence is Newton's sevenfold red, orange, yellow, green, blue, indigo and violet. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.




Visibility

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 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 color 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 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 airplane, 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 520°.

At good visibility conditions (for example, a dark cloud behind the rainbow), the second arc can be seen, with inverse order of colors. At the background of the blue sky, the second arc is barely visible.




Spectrum

A rainbow spans a continuous spectrum of colors - there are no "bands". The apparent discreteness is an artifact of the photopigments in the human eye and of the neural processing of our photoreceptor outputs in the brain. Because the peak response of human color receptors varies from person to person, different individuals will see slightly different colors, and persons with color blindness will see a smaller set of colors. However, the seven colors listed below are thought to be representative of how humans everywhere, with normal color vision, see the rainbow. The colors visible in the rainbow are not pure spectral colors. There is spectral smearing due to the fact that for any particular wavelength, there is a distribution of exit angles, rather than a single unvarying angle.

Newton originally (1672) named only five primary colors:
red, yellow, green, blue and violet.


Later he included orange and indigo, giving seven colors
by analogy to the number of notes in a musical scale.




Explanation

he 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.

The amount by which light is refracted depends upon its wavelength, and hence its color. 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 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 colors blend together rather than forming 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 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), and forms a circle 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 usually 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

Occasionally, a second, dimmer 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 degrees - 53 degrees. As a result of the second reflection, the colors 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 triple, 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.


Contrast-enhanced photograph of a supernumerary rainbow,
with additional green and purple arcs inside the primary bow.

Occasionally, another beautiful and striking rainbow phenomenon can be observed, consisting of several faint rainbows on the inner side of the primary rainbow, and very rarely also outside the secondary rainbow. They are slightly detached and have pastel color bands that do not fit the usual pattern. They are known as supernumerary rainbows, and 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, canceling each other out through destructive interference, and creating a gap. Given the different angles of refraction for rays of different colors, the patterns of interference are slightly different for rays of different colors, so each bright band is differentiated in color, creating a miniature rainbow. Supernumary rainbows are clearest when raindrops are small and of similar size. The very existence of supernumary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in 1804.


Primary and secondary rainbows are visible, as well as a
reflected primary and a faintly visible reflection primary.

Other rainbow variants are produced when sunlight reflects off a body of water. Where sunlight reflects off water before reaching the raindrops, it produces a reflection rainbow. These rainbows share the same endpoints as a normal rainbow but encompass a far greater arc when all of it is visible. Both primary and secondary reflection rainbows can be observed.

A reflected rainbow, by contrast, is produced when light that has first been reflected inside raindrops then reflects off a body of water before reaching the observer. A reflected rainbow is not a mirror image of the primary bow, but is displaced from it to a degree dependent on the Sun's altitude. Both types can be seen in the image to the right.




History of the Science of Rainbows

The Persian astronomer Qutb al-Din al-Shirazi (1236-1311), or perhaps his student Kamal al-din al-Farisi (1260-1320), is thought to have first given a fairly accurate explanation for the rainbow phenomenon.

The work of Robert Grosseteste 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 colors of the rainbow.

Theodoric of Freiberg is also 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" (quoted from David C, Lindberg, Roger Bacon's Theory of the Rainbow: Progress or Regress?, Isis, Vol. 57, no. 2, p. 235). He explained the secondary rainbow through a similar analysis involving two refractions and two reflections.





Rene Descartes' sketch of how primary and secondary rainbows are formed

Descartes, in 1637, further advanced this explanation. Knowing that the size of raindrops didn't 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 was able to back this up 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 colors, however, was based on a mechanical version of the traditional theory that colors were produced by a modification of white light.

Isaac Newton was the first to demonstrate that white light was composed of the light of all the colors of the rainbow, which a glass prism could separate into the full spectrum of colors, rejecting the theory that the colors 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 supernumary rainbows, and a satisfactory explanation was not found until Thomas Young realized 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 colors 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.


Rainbows




Rainbows in the News ...


In a "Rainbow" Universe Time May Have No Beginning   Scientific American - December 9, 2013

What if the universe had no beginning, and time stretched back infinitely without a big bang to start things off? That's one possible consequence of an idea called "rainbow gravity," so-named because it posits that gravity's effects on space-time are felt differently by different wavelengths of light, aka different colors in the rainbow. Rainbow gravity was first proposed 10 years ago as a possible step toward repairing the rifts between the theories of general relativity (covering the very big) and quantum mechanics (concerning the realm of the very small). The idea is not a complete theory for describing quantum effects on gravity, and is not widely accepted. Nevertheless, physicists have now applied the concept to the question of how the universe began, and found that if rainbow gravity is correct, space-time may have a drastically different origin story than the widely accepted picture of the big bang. According to Einstein's general relativity, massive objects warp space-time so that anything traveling through it, including light, takes a curving path.




Scientists Stop Light in 'Trapped Rainbow' Live Science - November 15, 2007

Scientists have worked out how to bring beams of light to a screeching halt inside a material that would separate the light into its constituent colors, creating a rainbow - a trapped rainbow. To bring light to a stop from its usual approximately 670 million mph (1.08 billion km/h) pace is no easy feat, and scientists have been working on the problem for years in hopes of revolutionizing how information is stored and sent. To tackle the challenge, physicist Ortwin Hess of the University of Surrey and his colleagues have devised a theoretical means to stop light using what are known as metamaterials, or materials whose properties depend on their structure and not the composition of the material.

The property of these materials that makes them ideal for stopping light is their "negative refractive index." The refractive index of a medium is a measure of how much light slows down and reorients or bends as it passes through the medium. Most materials, such as glass and water, have a positive refractive index - light keeps moving in basically the same direction. The negative refractive index of metamaterials (created by arranging tiny metallic inclusions in a transparent material) causes the light to bend somewhat back on itself and in such a way that "it gets slower and slower and eventually stops," Hess explained. (These same materials have been used to create an "invisibility cloak.")





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