Prisms and the Rainbow

Refraction

Before we get to prisms we should begin with the physics concept, refraction. Refraction describes the change in direction of a light ray when it passes into a different material. While all wavelengths of light move at c = 2.998⁸ m/s in a vacuum, they do not move at the same speed in materials (including air). The more densely packed with atoms the material is, the slower the light will be, as the light interacts with the electrons in the atoms. It is important to note that if the light ray hits the surface at a 90 degree angle, while it will change speed, it will not change direction. If the ray hits at any angle other than 90 degrees, its direction will change in the new material. The "slower" or "faster" the material is compared to the original, the greater the change. The index of refraction is a constant for one specific material, and it determines the angle of refraction.

The reason the light rays change direction when they hit a surface at an angle other than 90 degrees, is because light travels in waves. Because the speed of the wave changes and different peaks/valleys of the light ray hit the surface at the same time, the light has to bend in order for the wave peaks and valleys to stay intact. See the gif above for illustration.

Prisms

This illustration is from this wikipedia page

Prisms can split white light into its spectral components (the different wavelengths). Since the prism is a different material than air (such as glass or quartz), the photons travel at a slightly slower speed in said material. Even in the same material, different wavlengths of light will move at different rates through the material. This causes them to also go in different directions from each other. Different wavelenths of light have different frequencies (inversely proportional to wavelength), which determines the rate at which the waves move through a material (phase velocity). Violet light has the highest frequency (thus highest phase velocity) and red light has the lowest frequency (and phase velocity). Since violet wavlenegths have more frequent waves, it is more affected when it hits an angled surface. The slightly different direction these wavelegths go in separates them, allowing the individual colors to be seen rather than just white light. Note that if the surface is perpendicular to the light, the wavelengths will not separate, as the direction will not change.

Being the slowest wavelength, the red light path is the least changed by refraction, leading it to be "on top". Violet is the most affected, thus it is on bottom.

The shape of prisms

Most glass windows do not throw rainbows when direct sunlight passes through them, however many leaded glass windows will (at the right time of day). Likewise a cube (or any rectangular prism) of glass/crystal will not separate white light into colors, but a pyramid or triangular prism will. This is because a normal window or cube has parallel surfaces that the light enters and exits. When the light exits the parallel glass surface, the lights refraction as it passes back into air is the reverse of that as it entered the glass, stopping the divergence, meaning the colors have only seperated for as long as they were in the relatively thin glass. Because a pyramid or beveled edge does not have parallel surfaces, the light upon exiting the glass will be additionally refracted, separating the colors further.

In the diagram above, the parallel rainbows (through a parallel faced material) will overlap, creating white again, except at the very edges where a red-yellow edge may be observed on one side and a blue-violet edge on the other side. Conversely, the converging surfaces separate the colors enough that each color forms their own band, only overlapping near the surface of the prism

Here you can see a prism dispersing light into a rainbow, where the colors overlap closer to the prism. You can also see a triangle of light with a blue edge and a red edge, demonstrating the parallel surface example (though it was not produced by a parallel surface, it is likely the first surface was more perpendicular to the incoming light, thus the wavelengths were not refracted much, allowing them to overlap significantly).

Rainbows

So what do prisms have to do with the rainbows we see in the sky?

Basically, water droplets in the air act as prisms, splitting the white light from the sun into a spectrum of colors. Notice that the light is reflected by the inside of the water droplets. So the light enters the droplet, is reflected by the inside surface of the droplet, and then exits the droplet. Note that most of the light that enters the water drop passes right through it rather than reflecting, but this light does not form a rainbow, only those that are reflected within the drop do. This will be explained in an upcoming page.