What is a Rainbow?
Author Donald Ahrens in his text Meteorology Today describes a rainbow as "one of the most spectacular light shows observed on earth". Indeed the traditional rainbow is sunlight spread out into its spectrum of colors and diverted to the eye of the observer by water droplets. The "bow" part of the word describes the fact that the rainbow is a group of nearly circular arcs of color all having a common center.
This is a test link to an anchor point somewhere else on the page.Where is the sun when you see a rainbow?
This is a good question to start thinking about the physical process that gives rise to a rainbow. Most people have never noticed that the sun is always behind you when you face a rainbow, and that the center of the circular arc of the rainbow is in the direction opposite to that of the sun. The rain, of course, is in the direction of the rainbow.
What makes the bow?
A question like this calls for a proper physical answer. We will discuss the formation of a rainbow by raindrops. It is a problem in optics that was first clearly discussed by Rene Descartes in 1637. An interesting historical account of this is to be found in Carl Boyer's book, The Rainbow From Myth to Mathematics. Descartes simplified the study of the rainbow by reducing it to a study of one water droplet and how it interacts with light falling upon it.
He writes: Considering that this bow appears not only in the sky, but also in the air near us, whenever there are drops of water illuminated by the sun, as we can see in certain fountains, I readily decided that it arose only from the way in which the rays of light act on these drops and pass from them to our eyes. Further, knowing that the drops are round, as has been formerly proved, and seeing that whether they are larger or smaller, the appearance of the bow is not changed in any way, I had the idea of making a very large one, so that I could examine it better.
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What makes the colors in the rainbow?
The traditional description of the rainbow is that it is made up of seven colors - red, orange, yellow, green, blue, indigo, and violet. Actually, the rainbow is a whole continuum of colors from red to violet and even beyond the colors that the eye can see.
The colors of the rainbow arise from two basic facts:
- Sunlight is made up of the whole range of colors that the eye can detect. The range of sunlight colors, when combined, looks white to the eye. This property of sunlight was first demonstrated by Sir Isaac Newton in 1666.
- Light of different colors is refracted by different amounts when it passes from one medium (air, for example) into another (water or glass, for example).
Descartes and Willebrord Snell had determined how a ray of light is bent, or refracted, as it traverses regions of different densities, such as air and water. When the light paths through a raindrop are traced for red and blue light, one finds that the angle of deviation is different for the two colors because blue light is bent or refracted more than is the red light. This implies that when we see a rainbow and its band of colors we are looking at light refracted and reflected from different raindrops, some viewed at an angle of 42 degrees; some, at an angle of 40 degrees, and some in between. This is illustrated in this drawing, adapted from Johnson's Physical Meteorology. This rainbow of two colors would have a width of almost 2 degrees (about four times larger than the angular size as the full moon). Note that even though blue light is refracted more than red light in a single drop, we see the blue light on the inner part of the arc because we are looking along a different line of sight that has a smaller angle (40 degrees) for the blue.
What makes a double rainbow?
Sometimes we see two rainbows at once, what causes this? We have followed the path of a ray of sunlight as it enters and is reflected inside the raindrop. But not all of the energy of the ray escapes the raindrop after it is reflected once. A part of the ray is reflected again and travels along inside the drop to emerge from the drop. The rainbow we normally see is called the primary rainbow and is produced by one internal reflection; the secondary rainbow arises from two internal reflections and the rays exit the drop at an angle of 50 degrees° rather than the 42°degrees for the red primary bow. Blue light emerges at an even larger angle of 53 degrees°. his effect produces a secondary rainbow that has its colors reversed compared to the primary, as illustrated in the drawing, adapted from the Science Universe Series Sight, Light, and Color.
It is possible for light to be reflected more than twice within a raindrop, and one can calculate where the higher order rainbows might be seen; but these are never seen in normal circumstances.
Why is the sky brighter inside a rainbow?
Notice the contrast between the sky inside the arc and outside it. When one studies the refraction of sunlight on a raindrop one finds that there are many rays emerging at angles smaller than the rainbow ray, but essentially no light from single internal reflections at angles greater than this ray. Thus there is a lot of light within the bow, and very little beyond it. Because this light is a mix of all the rainbow colors, it is white. In the case of the secondary rainbow, the rainbow ray is the smallest angle and there are many rays emerging at angles greater than this one. Therefore the two bows combine to define a dark region between them - called Alexander's Dark Band, in honor of Alexander of Aphrodisias who discussed it some 1800 years ago!
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