Why does a rainbow contain a pure spread of spectral colors?
Category: Physics Published: January 30, 2014
A rainbow does not contain a pure spread of spectral colors, although it is somewhat close. A spectral color is a color that contains only one wavelength component of its electromagnetic wave. In contrast, a non-spectral color contains many wavelengths and is therefore a mixture of spectral colors. Simple lasers produce effectively pure spectral colors. The visible "electromagnetic spectrum" is a continuous spread of all of the spectral colors, arranged according to wavelength (i.e. red, orange, yellow, green, blue, and violet). Furthermore, the complete electromagnetic spectrum is a continuous spectrum and contains an infinite number of spectral colors. Just because we do not have a common name for the spectral color between red and orange does not mean that it is not a spectral color. When we display the spectrum of a certain light beam (or the spectrum of the light from a certain object), we are really just showing the spectral colors contained in that light, as well as their intensities and locations on the wavelength scale. Natural white light, such as from the sun, contains all spectral colors and therefore displays a continuous spread when separated into a pure spectrum of spectral colors (ignoring the narrow absorption lines). For instance, when white light enters and exits a glass prism, the different spectral color components of the light bend different amounts due to the dispersive nature of the glass. The different colors exit the prism at different angles, leading to a pure spectrum that becomes visible when it reflects off a wall or screen (strictly speaking, a prism only creates a pure spectrum if the original beam of light is very thin).
Unlike the spread of colors created by a prism, the spread of colors created by a spherical raindrop is not a pure spectrum. (By the way, raindrops are round and not tear shaped.) While the brightest part of a rainbow (the colorful outer edge) is close to a pure spectrum, each point in the spread contains a mixture of spectral colors. The more you look inwards from the outer edge of a rainbow, towards the arc's center, the more spectral colors there are mixed together, until finally the entire interior region of a rainbow is faint white, indicating a complete mix of all colors. The reason that a point in a rainbow contains a mix of spectral colors is ultimately because the front surface of a raindrop is round. This means that different parts of the original light beam encounter the raindrop's curved surface at different angles and bend different amounts, even for a single color. The diagram above shows how each color gets bent into many angles. Although pure red is mostly bent by a raindrop into a 42.1° viewing angle to form the outer edge of a rainbow, some of the red is bent into all angles between 0° and 42.1° because of the curved surface of the raindrop. Similarly, pure orange is mostly bent into the 41.9° viewing angle, but some orange is bent into all lower angles as well. The color in a rainbow at 42.1° is therefore red, the color at 41.9° is orange plus a little bit of red, the color at 41.7° is yellow plus a little bit of orange and red, etc. The end result is that the colors in a rainbow tend to blur together and wash each other out. The extended shape of the sun also sends light into the raindrop at slightly different angles and further blurs the colors together.
A prism and a raindrop are in principle very similar. They both spread white light out into a span of colors through refraction. The main difference though is that a prism has flat surfaces, leading to a pure spectrum, while a raindrop has a round surface, leading to an impure spectrum. Unfortunately, in everyday language, the phrases "rainbow" and "visible spectrum" are used to mean the same thing, even though scientifically, they are not exactly the same.