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Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind a person at a low altitude or angle (on the ground). The most spectacular rainbow displays happen when half of the sky is still dark with draining 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. Rainbow fringes can sometimes be seen at the edges of backlit clouds[1] and as vertical bands in distant rain or virga. The effect can also be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or night-time 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]
The rainbow's appearance is caused by dispersion of sunlight as it goes through raindrops. 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 'rain'bow 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 because the area of the back of the droplet has a focal point inside the droplet, the spectrum crosses itself, and therefore 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 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.
A rainbow does not actually exist at a particular location in the sky. It is an optical illusion whose 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 below), on top of a mountain, or above a waterfall. A rainbow can be generated using a garden sprinkler but to get sufficient drops they must be very small.
It is difficult to photograph the complete arc of a rainbow, 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 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. This phenomenon can be confused with the glory, but a glory is usually much smaller, covering only 5°–20°.
Occasionally, a second, dimmer, and thicker 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.
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”.[citation needed] 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.[citation needed] Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam.
Infrequently another rainbow phenomenon is 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 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.
Primary and reflection rainbow at sunset
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Primary and reflection rainbow at sunset
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. Such a rainbow shares the same endpoints as a normal rainbow but encompasses 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.
Another rainbow-like variant is produced when sunlight is reflected off clouds. The fire rainbow or circumhorizontal arc can sometimes be seen in cirrus clouds with ice crystals (normally at least 6 km above sea level) and with the sun at least 58° above the horizon.
You can create your own rainbow by facing 180 degrees from the sun and spray mist from a garden hose in front of you in a circular motion, outlining a 360 degree "rainbow".