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 colours are present in some form, but only one tertiary colour. 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 colours in the blue portion of the visual spectrum.
The rainbow effect can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude or angle. The most spectacular rainbow displays when half of the sky is still dark with draining clouds and the observer is at a spot with clear sky overhead. Another common place to see the rainbow effect is near waterfalls. Rainbow fringes can sometimes be seen at the edges of backlit clouds 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.
In a very few cases, a moonbow, or night-time rainbow, can be seen on strongly moonlit nights. As human visual perception for colour in low light is poor, moonbows are perceived to be white.
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, and hence 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 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; however, light that emerges from the back of the raindrop does not create a rainbow between the observer and the Sun. The 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 and do not form a rainbow.
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. 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 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.
Sometimes, a second, dimmer secondary 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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