A rainbow spans a continuous spectrum of colours. Traditionally, however, the sequence is quantised. The most commonly cited and remembered sequence, in English, is Newton's sevenfold red, orange, yellow, green, blue, indigo, and violet. "Roy G. Biv" and "Richard Of York Gave Battle In Vain" are popular mnemonics.

Rainbows can be caused by other forms of water than rain, including mist, spray, dew, fog, and ice. Moreover, rainbows can have shapes other than a bow (arc), including stripes, circles, or even flames. (See circumhorizontal arc).

Visibility

The rainbow effect is also commonly seen near waterfalls or fountains. Rainbow fringes can sometimes be seen at the edges of backlit clouds1 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.

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 wide-angle lens would be required. 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°.

Scientific explanation

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 'rainbow' in sea spray is smaller than a true rainbow. This is visible to the naked eye by a misalignment of these bows.

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.