Rainbows are one of earth's most widely occurring atmospheric phenomena. Breathtaking to behold, meteorologist Donald Ahrens has described them as "one of the most spectacular light shows observed on earth." From ancient cultures to modern times, these mysterious multicolored arcs have captivated the imaginations of artists, poets, and scientists for thousands of years. However, the mechanisms that create them have been unraveled and their secrets deduced granting us insight into one of nature's most inspiring wonders. Science has afforded us an opportunity to appreciate more fully the majesty of one of nature's most beautiful creations.
In order to understand where and why a rainbow comes into being, we must first understand three basic premises: the nature of light and color, the optical properties of raindrops, and the effect of observation. To begin with, the light from the sun is a collection of long and short waves that make up all the colors we can see (and some we can't see); the longest waves are red, the shortest are violet. When the light reaches earth all the wavelengths are together, combining the colors and making the light from the sun white. The visible colors of the rainbow are red, orange, yellow, green, blue, indigo and violet.
The reason we know that sunlight is composed of many colors is that in 1672, Sir Isaac Newton discovered that by shining sunlight through a prism it could be refracted and dispersed into its constituent light bands. These light bands, when shined onto a second prism designed to recombine them, became the same light as the sun sheds once again. This is also why objects are colorful: a red object on which sunlight shines absorbs the shorter waves of light and reflects only the longer red light bands for our eyes to detect.
Rainbows spring into being because the water in raindrops disperses the color bands in sunlight like a prism does, but in a different way. As water falls through the air, it assumes a spherical shape between a few millimeters and one-hundredth of a millimeter in diameter. When sunlight hits the raindrop some of it is reflected and some of it enters the raindrop and is refracted at a particular angle. Once the light reaches the other side of the raindrop, some is reflected back and refracted again when it leaves the raindrop. During this process the light is partially dispersed into its color bands, the longer bands dispersing more while the shorter bands disperse less.
Because earth is so far from the sun, all of the light from it effectively travels in the same direction, causing the light that is refracted by the raindrop to all refract to the same degree relative to the sun. We see the light spectrum when the refracted and reflected light leaving the raindrop hits our eye from the correct angle for us to see the prism created by the dispersal. That we can only see the light bands from one angle causes it to appear to us as circle, the center of which is the point exactly opposite the sun (the majority of the circle obscured by the ground, hence the "bow" shape). Because of this, we can only see rainbows when the sun (or in rarer cases, the full moon) shines from behind us onto raindrops in front of us.
As to how we discovered this, in 1637 the mathematician Rene Descartes was able to discover the angle at which a rainbow must appear. Knowing that raindrops fell as spheres, and having observed that rainbows are created by fountains as well as natural rainfall, he constructed a glass sphere that he filled with water. Looking into it as sunlight shined through, he realized that he could see the water change color as he moved it about his head. Through numerous tests he deduced that, regardless of the sphere's position in relation to his eye, he could only see the colors of light when the orb of water was at an angle of 42 degrees in relation to the sun. He deduced that a rainbow exists at the base of a cone: its tip our eye, it's base as far away as the furthest, sunlit raindrop at the correct angle.
A rainbow, it turns out, is not so much a beautiful thing we see as it is a beautiful illusion created by our eye when rain and sunlight come together in the correct measurements. It is a beautiful thing created by the way we see. However, simply knowing these facts does not explain everything about rainbows. There are several niceties that have yet to come to light which we must explore before we can be satisfied.
When rainbows are created, a second, less-distinct rainbow is often visible outside the well-defined primary rainbow. This rainbow exists for the same basic reasons as the first, but applied differently. Where the primary rainbow is created when sunlight is reflected off the far side of a raindrop, the light that creates the second rainbow is reflected again when it reaches the near side, and again when it reaches the far side once more. Because this light has been bouncing around the inside of the raindrop, it has been refracted more and the spectrum it creates appears at an angle of 50 degrees rather than 42 degrees. It appears larger because the angle at which it is visible to the eye is steeper; it appears dimmer because less light is refracted this way than in the primary rainbow's case.
A strange type of rainbow, one which is at once a double rainbow and not, is a reflection rainbow. Reflection rainbows occur when two sources of sunlight shine on the same rainfall, such as when sunlight is reflected from the surface of a lake. When this occurs, two rainbows are usually formed, one from the direct light of the sun, and one from the reflected light. However, the light reflected by the lake has a different point of origin from the light coming directly from the sun. What this means is that the reflection rainbow's center will be higher relative to the horizon, more of the circle will be visible, and the two rainbows will overlap. This does not mean that the light is refracted differently by the raindrops, the rainbow still exists only at a 42 degree angle. What it means is that the point that is opposite the source of light is higher relative to our eye's point of view.
Another peculiar aspect of some rainbows are ripples within the rainbow that are not a part of the rainbow's spectrum. Rainbows with these odd sub-spectra are called supernumerary rainbows and they exist due to interference that occurs within the raindrop when the light is dispersing into its spectrum. When a rainbow is created, light is not only coming from the direction of the sun, but is also being reflected and refracted by water droplets. The light within one raindrop that is part of the group creating the rainbow is bombarded by light from other raindrops that can interfere with its path and strength. This phenomenon occurs most commonly in rainbows created by comparatively big raindrops, their larger size giving the disparate light waves more time to interact. The Brazillian physicist Herch Nussenzveig described the process succinctly:
"At angles very close to the rainbow angle the two paths through the droplet differ only slightly, and so the two rays interfere constructively. As the angle increases, the two rays follow paths of substantially different lengths. When the difference equals half of the wavelength, the interference is completely destructive; at still greater angles the beams reinforce again. The result is a periodic variation in the intensity of the scattered light, a series of alternately bright and dark bands."
One more interesting observation concerning rainbows is that the sky within a rainbow appears brighter than the sky surrounding it. The darkness without the rainbow is called Alexander's Dark Band in honor of Alexander of Aphrodisias, an ancient Greek philosopher who was first to describe it in writing sometime in the 3rd Century C.E. The dark band appears because the raindrops that create the rainbow are refracting light primarily toward the center of the rainbow. The light waves that do not appear to our eyes as color bands continue as visible light, illuminating the area inside the rainbow and giving the sky behind it the appearance of being brighter
Of course, we have barely touched on the subject of rainbows and many more questions are left to be answered. Below are some common rainbow questions that were addressed in W.J. Humphreys' "Physics of the Air:"
"It is nearby or far away, according to where the raindrops are, extending from the closest to the farthest illuminated drops along the elements of the rainbow cone."
"To see a rainbow, one has to have rain and sunshine. In the winter, water droplets freeze into ice particles that do not produce a rainbow but scatter light in other very interesting patterns."
"Remember that the center of the rainbow's circle is opposite the sun so that it is as far below the level of the observer as the sun is above it."
"Since the rainbow is a special distribution of colors (produced in a particular way) with reference to a definite point-the eye of the observer-and as no single distribution can be the same for two separate points, it follows that two observers do not, and cannot, see the same rainbow."
"On the basis of the arguments given in the receeding question, bows appropriate for two different points are produced by different drops; hence, a bow seen by reflection is not the same as one seen directly."
In the last five-hundred years we have come a long way in understanding the workings of the world. That we now know how something so magical-seeming in nature is created by the interaction of light, water, and our eyes might seem to some to take some of the wonder out of rainbows. However, if we consider the method by which rainbows are created-as an optical illusion produced in the eyes of the observer-it seems more that what we have really done is discover that what we once believed to be a beautiful object in nature is actually a bit of beauty within each of us.
There are a number of rainbow and light-spectrum based experiments that can be undertaken in a classroom. Here are a few that are basic and easy to setup.