A page from the "Causes of Color" exhibit...
Why are rainbows & prisms spectra colored? (dispersive refraction)
The spectral colors of the rainbow are caused by dispersive refraction
Newton established that refraction causes the dispersion of light into its constituent hues. He named seven colors, in symmetry with the seven distinct notes in the Western musical scale.
Rainbows, with their ephemeral quality and gorgeous hues, have fascinated us since the beginning of recorded time. The rainbow is deeply rooted in our history. It appears in the oldest of stories, as well as being ubiquitous in art and music.
Newton and the color spectrum: dispersive refraction
Isaac Newton established that refraction causes white light to separate into its constituent wavelengths. While he was not the first to demonstrate that a prism produces a spectrum of colored light from incident white light, he showed that a second prism could recombine the colors to create white light again. He also demonstrated that the individual colors remained constant when shone through a prism again. This was in stark contrast to the consensus that the prism itself produced colors.
Newton’s contribution created a new understanding that white light is a mixture of colored light, and that each color is refracted to a different extent. The different colors correspond to light with different wavelengths, and are refracted to differing degrees. This separation of colors is known as dispersion.
Once the colors in sunlight are separated by refraction, we are able to distinguish them in the splendor that is a rainbow.
What is refraction?
The refractive index (n) of a medium such as air or water tells us how fast light travels in that medium. It is the ratio of the speed of light in a vacuum (c) to the speed of light in this medium (v): n = c / v.
The bending of a light as it crosses the boundary into a different medium is determined by its refractive index, or how much the light is slowed down in the new medium.
We see objects "breaking" at the boundary between media of different density because of refraction. Light rays are bent, or refracted, because light travels at different speeds in different media. Unless the light ray meets the boundary at exactly 90°, the direction of travel will change and the light ray is "bent."
The relationship between the angle of incidence and speed in the first medium and the angle of refraction and the speed of the refracted light in the second medium is given by Snell’s law: n1 sin θ1 = n2 sin θ2 (where θ1 = incident angle, n1 is the refractive index of the first medium, θ2 = refracted angle, and n2 is the refractive index of the second medium).
The reason that light travels more slowly in a higher density medium is that light interacts with the particles in its path. When light traveling through space to the earth meets the atmosphere, light is absorbed and then re-emitted every time a photon of light collides with an atom of air.
Rainbows can be seen in the spray of a waterfall. Ideal conditions for rainbows are sunlight and water droplets, usually as rain, but also in fine spray.
How is a rainbow formed?
The mechanics of rainbows have been studied since ancient times. The Greek philosophers were aware of the role of reflection in forming a rainbow, and had some understanding of the role of refraction. In the 13th century, scientists produced theories on rainbow formation, and in the 17th century, Rene Descartes sketched out the conditions required to observe a rainbow.
We see rainbows because of the geometry of raindrops. When the sun shines from behind us into the rain, incident rays of light enter the drop and are refracted inwards. They are reflected from the back surface of the raindrop, and refracted again as they exit the raindrop and return to our eyes. Refraction is responsible for splitting the sunlight into its component colors.
Descartes’ well-known sketch describes the conditions required to observe a rainbow. The sun is directly behind him, and the light reflected from the raindrops ahead of him concentrates between approximately 40.6° and 42.4°, centered on the point where the shadow of his head would be.
You perceive a rainbow from a particular position; "your" rainbow will alter as you move and will differ from others’ perceptions. Because the light from any single drop is dispersed, only one ray of a particular color reaches your eye. The violet band that you see leaves the corresponding raindrops at about 40.6°, and the red band that you see leaves its corresponding raindrops at 42.4°, so the red light is from raindrops higher in the sky relative to your eye.
If we were able to see an entire rainbow (for example from a plane) it would form a full circle. This rainbow over the Iguazu Falls illustrates this with its extended arc.
The size of the raindrops does not affect the geometry of the rainbow, although very tiny drops, such as those in fog or mist, reduce the effect. In this case, the effect of scattering overpowers the dispersive refraction effect. A "fogbow" has the arc of a rainbow, but appears as a bright white bow without spectral colors.
The angle of the sun does affect the rainbow we see. Once the sun is higher than 42°, the rainbow arc slips below the horizon. As the sun approaches the horizon, the size of the visible arc increases, reaching a full semicircle just before sunset.
Moonbows have been observed, but as our night vision is not sensitive to color, they appear white rather than colored.
Secondary rainbows are formed by double internal reflection. Light is reflected twice from the inner surface of the raindrop before leaving the raindrop. The light is concentrated between approximately 50.4° and 53.6°, forming a secondary rainbow above the primary rainbow.
Secondary rainbows and supernumerary rainbows
If one rainbow is beautiful, a double rainbow is breathtaking. In fact, is possible for sunlight to be reflected three or more times in one raindrop, but third order rainbows cannot be seen. They form so close to the sun that its brightness overpowers them.
In the laboratory, it is possible to recreate multiple rainbows formed by multiple internal reflections. A spherical flask of water simulates the raindrop.
The Blind Girl, by John Everett Millais, expresses the pathos of this figure, unaware of the splendor surrounding her. The artist has taken some liberties with the double rainbow here; the dramatic dark sky below the rainbow does not occur in nature.
In a double rainbow, raindrops reflect the sun’s light noticeably inward from the rainbow arc, and correspondingly out of the secondary bow, so that the dark band is seen between the bows. This effect, called Alexander’s band, was first described by the Greek philosopher Alexander of Aphrodisias in the 3rd century. The sky below the primary (lower) rainbow, and above the secondary (higher) bow, is brighter as a result.
This photograph illustrates the actual appearance of a double rainbow, with the bright area below the primary bow and the dark Alexander band between the bows. The colors of the bright primary rainbow (lower) run from violet on the inside to red on the outside. In the secondary (higher) rainbow the color sequence is reversed, with red on the inside and violet on the outside.
A supernumerary rainbow forms additional bands on the inner arc of the primary rainbow, or very occasionally on the outer arc of the secondary rainbow. These bands, which usually appear in pastel colors, are caused by the interference of light waves.
The primary rainbow is brightest, with red at the top and violet at the bottom. The supernumerary bands appear up against the violet band, in pastel shades that do not follow the usual pattern of spectral color. These bands are caused by the interference of light waves, providing evidence for the wave nature of light.