A rainbow is a naturally occurring phenomenon that results from the way sunlight interacts with droplets of water in the air. While drawings often depict the multicolored arc of a rainbow as clear bands of different colors, a real rainbow is actually a continuous spectrum of the colors of visible light.
The colors of visible light, often referred to as ROY G BIV (for red, orange, yellow, green, blue, indigo, and violet), are a small portion of the entire electromagnetic spectrum. Light can be thought of as a stream of packets of energy called photons. The amount of energy contained in the photons determines the type of light. For example, photons of red light have less energy than photons of blue light. Alternatively, the light can also be described in terms of wavelength. For example, red light has a longer wavelength than blue light.
The range of energy and wavelength of visible light allows us to see rainbows. When light crosses the boundary between two materials, it changes speed. As a result, the path of light bends as it crosses the boundary—it is refracted. The angle at which it bends depends on both the material and the wavelength of the light. Different wavelengths of light bend at different degrees when passing into a new medium.
White light is a mixture of different wavelengths of light. As a result, when white light passes through a material such as a glass prism, each wavelength is refracted at a slightly different angle. This phenomenon is known as dispersion; the different angles of refraction separate the light into its constituent colors so that instead of seeing white light exit the prism, we see a spectrum of colors.
This is the same principle that creates rainbows. Although the process is more complicated than a single refraction—it also involves reflection—the basic idea is the same. As sunlight passes the boundary between the air and a droplet of water, it is refracted and dispersed into its constituent colors. When sunlight interacts with many droplets of water, you can see a rainbow.
To learn more about how light travels, check out The Light Stuff and Observing Refraction of Light.
To learn more about refraction, check out Refraction of Light Demonstration, Laser Waterfall, and Geometric Optics.
To learn more about the electromagnetic spectrum, check out The Electromagnetic Spectrum: FRONTLINE and The Electromagnetic Spectrum: NASA.
To learn more about colors, check out Primary Colors of Light and Pigments.