Rainbow

A rainbow is an arc-shaped spectrum of light created by refraction and reflection.

A rainbow demonstrates the dispersion of light and is evidence that visible light is composed of a spectrum of wavelengths.

A rainbow is not an object in a particular place but an optical phenomenon that depends on the viewer's position. The Sun must be behind the observer and water droplets in front. To view a rainbow the observer's back must be to the sun while looking about 40 degrees above the ground into droplets or mist.

Rainbows are always opposite the Sun and their centres lie below the horizon at the antisolar point, so the lower the Sun the higher the bow. The apparent centre of a rainbow is the shadow of the observer's head, so each person sees a slightly different bow.

Rainbows are not seen at midday because the whole 42 degree circle lies below the horizon at most latitudes.

From an airplane the entire circle of a rainbow can be seen because droplets may be falling both above and below the observer.

A ray of sunlight entering a raindrop is bent toward the normal as it crosses the surface, turned back by an internal reflection, and bent again as it leaves, this time away from the normal. Each droplet thus behaves as a minute prism that separates light into its constituent colours and returns it toward the observer.

The separation arises because refraction depends on wavelength: blue and violet light of shorter wavelength refract slightly more than longer-wavelength red light. Within a droplet violet, the shortest visible wavelength, bends the most, while red, the longest, bends the least.

The outgoing rays are most densely gathered at angles of deviation between 40 and 42 degrees. The reflection at the back of the drop contributes no dispersion of its own, since the law of reflection does not depend on wavelength.

Because the droplets need only hang in the air, waterfalls and garden sprinklers can produce rainbows as readily as falling rain.

For a given medium the index of refraction increases as wavelength decreases and is greatest for violet light; in water it rises from 1.331 for red light at 660 nanometres to 1.342 for violet light at 410 nanometres.

Red light leaves the drop at a deviation of about 42 degrees and violet at about 40, which places red on the outside of the primary bow.

The primary bow is the brighter of the two arcs Newton describes, formed by a single internal reflection within the raindrops. Its colours run from red on the outside of the arc to violet on the inside.

The band is not evenly bounded: its inner edge is diffuse while its outer edge is sharp. Newton popularised seven distinct colours, yet a rainbow actually contains a continuous range of hues.

A rainbow is not just a set of coloured rings: the sky inside is bright because raindrops direct light there too, making the primary a disk that brightens toward its rim.

The secondary bow is fainter because light is lost at each internal reflection, about twice as wide as the primary, and appears at a radius of about 51 degrees, roughly 9 degrees outside the primary.

The colour order of the secondary bow is reversed because sunlight is reflected twice inside the drop, with red on the bottom and violet on the top, so that the reds of the two bows face one another.

Alexander's band is the darker sky between the two bows, where no reflected light reaches the eye; it is named after Alexander of Aphrodisias, who described it some 1800 years ago.

Its outer edge is diffuse while its inner edge is sharp, the reverse of the primary bow.

Supernumerary arcs appear as interference fringes along the inner edge of the primary bow, closely spaced greenish and purple arcs lying on the inner, blue side.

Classical ray theory predicts extra brightness where two rays of equal deviation meet, but the waves can arrive out of phase and cancel instead. As the deviation angle changes the paired waves alternately reinforce and cancel, producing light and dark fringes whose bright fringes are supernumerary bows.

The tertiary bow is centred on the Sun and appears sunwards, so the observer must look back toward the Sun to see it. Its radius is given as 40 degrees 20 minutes around the Sun in one treatment and as a nominal 42.5 degrees in another, with the latter also assigning it about 24 percent of the primary's brightness.

The first photograph of a natural third-order bow was taken on 15 May 2011 by Michael Grossmann in south-west Germany. In the laboratory, orders up to thirteen have been produced with a laser and water droplets.

White light passing through a triangular prism separates into red, orange, yellow, green, blue and violet. The separation begins at the first face of the prism and increases at the second face. The angle of deviation varies with wavelength because the indices of refraction differ.

About six colours are seen in a rainbow, red, orange, yellow, green, blue and violet, with indigo sometimes added. The colour sequence follows the same order as the colours plotted against wavelength.

A rectangular prism reverses the refraction at exit, leaving only thin red and violet fringes rather than a spread spectrum.

Kamal al-Din al-Farisi worked in Persia from 1267 to 1319 and built an enormous water drop to study how droplets split white light.His experiments belong to a tradition of optical inquiry in which Theodoric of Freiberg performed similar optical experiments, and both he and al-Farisi relied on the work of Ibn al-Haytham.

Descartes gave a rough explanation of rainbows but did not account for supernumerary arcs, which need the wave theory that Airy applied with reasonable accuracy in about 1838 to explain them.

Newton passed a thin beam of sunlight through a glass prism and argued that white light is a mixture of rays refracted at slightly different angles.

Aristotle held that the rainbow came from sunlight reflected by the surface of a cloud, its colours a mixture of light and darkness.

Newton computed the red-ray angles of both bows and measured their angular widths, fixing the geometry that later measurements have largely confirmed.^{8Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light · Isaac Newton, Project Gutenberg edition of the 1730 fourth edition ↗}

A moonbow requires a nearly full low Moon, a dark sky and rain opposite the Moon. To the unaided eye a moonbow usually appears without colour because its light is too faint to activate the cone receptors.

Fogbows form in fog, mist or cloud, where droplets much smaller than raindrops diffract the light and smear out the colours, so a bow in droplets below 0.05 mm turns white.

A rainbow belongs to a family of large coloured circular arcs produced when light falls on a population of water drops. Within this family the supernumeraries appear inside the primary bow, and reflection bows complete the group.

The term rainbow is not applied to the corona and glory seen around the Sun and the antisolar point, nor to halos formed by ice crystals.

Iris was the goddess of the rainbow and the messenger of the Olympian gods. Servius held that the rainbow is only the road on which Iris travels, appearing when the goddess wants it and vanishing when it is no longer needed.

In Genesis the bow set in the cloud serves as the sign of a covenant between the deity and the earth.