A rainbow does not actually exist at a location in the sky, but rather is an optical phenomenonantisolar 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. As a result, if the Sun is higher than 42°, then 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. 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. 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

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°, as opposed to over 80° for a full circle rainbow. Occasionally, a second, dimmer secondary rainbow is seen outside the primary bow. Secondary rainbows are caused by a double reflection 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 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.

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

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

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 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. 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.

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.

Rainbows in religion and mythology
Main article: Rainbows in mythology

The rainbow has a place in legend due to its beauty and the difficulty in explaining the phenomenon before the work of Descartes in the 17th century (although, as mentioned above, Theodoric of Freiburg had given a satisfactory explanation in the 13th century.)

In Greek mythology, the rainbow 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 of Indra, the God of lightning and thunder. 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 crock of gold is usually said to be at the end of the rainbow (which, of course, one can never reach). In the Hebrew Bible, the rainbow is a symbol of the covenant between God and man, and God's promise to Noah that He would never again flood the entire Earth.