Rainbow
If the Sun were a laser emitting parallel, monochromatic rays, then the luminance (brightness) of the bow would tend toward infinity at this angle if interference effects are ignored (see Caustic (optics)).
[25] Conversely, at lower latitudes near midday (specifically, when the sun's elevation exceeds 42 degrees) a rainbow will not be visible against the sky.
Technically the secondary bow is centred on the sun itself, but since its angular size is more than 90° (about 127° for violet to 130° for red), it is seen on the same side of the sky as the primary rainbow, about 10° outside it at an apparent angle of 50–53°.
[33] A numerical ray tracing study showed that a twinned rainbow on a photo could be explained by a mixture of 0.40 and 0.45 mm droplets.
Viewing the rainbow's lower half requires the presence of water droplets below the observer's horizon, as well as sunlight that is able to reach them.
[38] It is possible to produce the full circle when standing on the ground, for example by spraying a water mist from a garden hose while facing away from the sun.
Another atmospheric phenomenon that may be mistaken for a "circular rainbow" is the 22° halo, which is caused by ice crystals rather than liquid water droplets, and is located around the Sun (or Moon), not opposite it.
In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i.e., inside the primary bow or, much more rarely, outside the secondary.
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.
When a rainbow appears above a body of water, two complementary mirror bows may be seen below and above the horizon, originating from different light paths.
[45][46] Occasionally a shower may happen at sunrise or sunset, where the shorter wavelengths like blue and green have been scattered and essentially removed from the spectrum.
A sleetbow forms in the same way as a typical rainbow, with the exception that it occurs when light passes through falling sleet (ice pellets) instead of liquid water.
[citation needed] The circumzenithal and circumhorizontal arcs are two related optical phenomena similar in appearance to a rainbow, but unlike the latter, their origin lies in light refraction through hexagonal ice crystals rather than liquid water droplets.
Since salt water has a higher refractive index, a sea spray bow does not perfectly align with the ordinary rainbow, if seen at the same spot.
[68] According to Raymond L. Lee and Alistair B. Fraser, "Despite its many flaws and its appeal to Pythagorean numerology, Aristotle's qualitative explanation showed an inventiveness and relative consistency that was unmatched for centuries.
"[69] In Book I of Naturales Quaestiones (c. 65 AD), the Roman philosopher Seneca the Younger discusses various theories of the formation of rainbows extensively, including those of Aristotle.
He even speaks of rainbows produced by small rods (virgulae) of glass, anticipating Newton's experiences with prisms.
[70] According to Hüseyin Gazi Topdemir, the Arab physicist and polymath Ibn al-Haytham (965–1039 AD) attempted to provide a scientific explanation for the rainbow phenomenon.
[72] In Song dynasty China (960–1279), a polymath scholar-official named Shen Kuo (1031–1095) hypothesised—as a certain Sun Sikong (1015–1076) did before him—that rainbows were formed by a phenomenon of sunlight encountering droplets of rain in the air.
[73] Paul Dong writes that Shen's explanation of the rainbow as a phenomenon of atmospheric refraction "is basically in accord with modern scientific principles.
"[74] According to Nader El-Bizri, the Persian astronomer, Qutb al-Din al-Shirazi (1236–1311), gave a fairly accurate explanation for the rainbow phenomenon.
[71][c] As he noted in his Kitab Tanqih al-Manazir (The Revision of the Optics), al-Farisi used a large clear vessel of glass in the shape of a sphere, which was filled with water, in order to have an experimental large-scale model of a rain drop.
Knowing that the size of raindrops did not appear to affect the observed rainbow, he experimented with passing rays of light through a large glass sphere filled with water.
He supported this conclusion with a derivation of the law of refraction (subsequently to, but independently of, Snell) and correctly calculated the angles for both bows.
Young's work was refined in the 1820s by George Biddell Airy, who explained the dependence of the strength of the colours of the rainbow on the size of the water droplets.
In Norse mythology, the rainbow bridge Bifröst connects the world of men (Midgard) and the realm of the gods (Asgard).
Cuchavira was the god of the rainbow for the Muisca in present-day Colombia and when the regular rains on the Bogotá savanna were over the people thanked him, offering gold, snails and small emeralds.
[95] Generalised examples in coat of arms include those of the towns of Regen and Pfreimd, both in Bavaria, Germany; of Bouffémont, France; and of the 69th Infantry Regiment (New York) of the United States Army National Guard.
[96] In 1994, Archbishop Desmond Tutu and President Nelson Mandela described newly democratic post-apartheid South Africa as the rainbow nation.
[97] In Saudi Arabia and other similar-minded countries, authorities seize children's clothing (including hats, hair clips, pencil cases, etc.)
