Rainbow

A rainbow is an optical and meteorological phenomenon that causes a nearly continuous spectrum of light to appear in the sky when the sun shines onto falling rain. It is a multicoloured arc with red on the outside and violet on the inside. The full sequence of colours is most commonly cited as red, orange, yellow, green, blue, indigo, and violet, though it is important to note that this is an inconsistent list; all primary and secondary colors are present in some form, but only one tertiary. It is commonly thought that indigo was included due to the different religious connotations of the numbers six and seven at the time of Isaac Newton's work on light, despite its lack of scientific significance and the poor ability of humans to distinguish colors in the blue portion of the visual spectrum.

Physics of rainbows

The rainbow's appearance is caused by dispersion of sunlight as it is refracted by (approximately spherical) raindrops. The light is first refracted as it enters the surface of the raindrop, reflects off the back of the drop, and is 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 about 40°–42°, regardless of the size of the drop. Since the water of the raindrops is dispersive, the amount that the sunlight is bent depends upon the wavelength (colour) of the light's constituent parts. Blue light is refracted at a greater angle than red light, but because the area of the back of the droplet has a focal point inside the droplet, the spectra crosses itself, and thus the red light appears higher in the sky, and forms the outer colour of the rainbow. Contrary to popular belief, the light at the back of the raindrop does not undergo total internal reflection; however, light that emerges from the back of the raindrop does not create a rainbow between the observer and the sun. This is because the emitted spectra there do not have a maximum of intensity, as the other visible rainbows do. Thus the colours blend together and do not form any rainbow.

Related Topics:
Dispersion - Refracted - Raindrops - Reflects - Angle - Wavelength - Blue - Spectra - Total internal reflection

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A rainbow does not actually exist at a location in the sky, but is an optical phenomenon whose apparent position depends on the observer's location. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. These raindrops are perceived to constitute the rainbow by that observer. Its position is always in the opposite direction of the sun with respect to the observer, and the interior is actually a magnified image of the sun, which can be seen to be 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 approximately 40°–42° to the line between the observer's head and its shadow (this means that if the sun is higher than 42° the rainbow is below the horizon and cannot be seen unless the observer is at the top of a mountain or a similar vantage point). Similarly it is difficult to photograph the complete arc of a rainbow, which would require an angle of view of 84°. For a 35 mm camera, a lens with a focal length of 19 mm or less would be required, whilst most photographers are only likely to have a 28 mm wide-angle lens. From an aeroplane one has the opportunity to see the whole circle of the rainbow, with the plane's shadow in the centre.

Related Topics:
Antisolar point - Angle of view - 35 mm - Wide-angle lens - Aeroplane

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Sometimes, a second, dimmer rainbow is seen outside the primary bow, caused by a double reflection of the sunlight inside the raindrops, and appears at an angle of 50°–53°. Because of the extra reflection, the colours of the bow are inverted compared to the primary bow, with blue on the outside and red on the inside. Alexander's band is an area of unlit sky lying between the primary and secondary bows.

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A triple rainbow is even more rarely seen. 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 harder to spot.

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Occasionally, another beautiful and striking rainbow phenomenon could 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 colour bands that do not fit the usual pattern. They are known as supernumerary rainbows, and their very existence was historically a first indication of the wave nature of light.

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Other rainbow variants are ones produced when the sunlight reflects off a body of water before reaching the raindrops. This produces a reflection rainbow which shares the same endpoints as the normal one but encompasses a far greater arc when all of it is visible. Reflection rainbows can exist for both the primary and secondary. A reflected rainbow is produced when light that has been reflected inside the raindrops reflects off a body of water before reaching the observer. It is not a mirror image of the primary, being displaced from it to a degree dependent on the sun's altitude. In the image below both types can be seen. The reflection rainbow is faintly visible curving between the primary and secondary, and the reflected rainbow can be seen in the water.

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The Persian astronomer Qutb al-Din al-Shirazi is thought to have first given a fairly accurate explanation for the rainbow phenomenon. Theodoric of Freiberg is also known to have given an accurate theoretical explanation of the rainbow in 1307; he postulated that when sunlight falls on individual drops of moisture, the rays undergo two refractions (upon ingress and egress) and one reflection (at the back side 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. 236.).

Related Topics:
Qutb al-Din al-Shirazi - Theodoric of Freiberg

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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. However, he was unable to explain the colours.

Related Topics:
Descartes - 1637 - Refraction - Snell

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Isaac Newton was the first to demonstrate that white light was composed of the light of all the colours of the rainbow, which a glass prism could split into the full spectrum of colours. He also showed that red light gets refracted less than blue light, which led to the first scientific explanation of the major rainbow features.

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Advances in computational methods and optical theory continue to lead to a fuller understanding of rainbows. The article by Nussenzveig listed in the references provides a modern overview.

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