A rainbow is one of our atmosphere’s most exquisite and marvelous creations; “one of the most spectacular light shows observed on earth” (Ahrens, 1998). When a person views a rainbow, they are getting a personal light show that no other person can see as they do. Humphreys points out that:
“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.” (Humphreys, 1929).
Of course, a camera lens will record an image of a rainbow which can then be seen my many people (Lynds, 1995).
A rainbow is essentially made up of seven brilliant colors: red, orange, yellow, green, blue, indigo, and violet; moreover, it is comprised of many coloration that the eyes cannot see. No painter can manufacture the colors of the rainbow, for they create color by mixing, but no mixing will give red, green, or purple. These are the colors of the rainbow, though between the red and the green an orange color is often seen (Aristotle, 350 BC). To understand how the awesome production of a rainbow occurs is a feat of physics and mathematics. The two most important ingredients are light and drops of water. The manner and position in which the light and water droplets transverse, and the reactions between the two, are complex formulas of nature. Additionally, certain circumstances make it possible for a rainbow to occur.
You cannot have a rainbow without some source of light. It is possible to create an artificial rainbow utilizing artificial light, but for this paper, I will only use instances and circumstances of naturally occurring light which produce naturally occurring rainbows. The sun is nature’s primary source of rainbow creating light; however, occasionally, the light of the moon can produce a rainbow. For a lunar rainbow to occur the conditions have to be just right. The moon has to be a full moon, which only happens once a month. The light of a full moon is a faint light, so the lunar rainbow will never be as prominent as the solar rainbow. Additionally, the full moon has to be either rising or setting. A naval officer, V. E. Mikkelson, described his reaction when he learned that the spotlight he saw was actually a lunar rainbow:
The strange phenomenon I was viewing was a rainbow generated by moonlight! It was being formed by moonlight passing through rain trailing from one of the fluffy cumulus clouds. The rainbow was composed of the standard colors, but they were softer and paler than those generated by direct sunlight. They were what I can only describe as pastel. I was truly entranced. I have seen many of nature’s beauties, but none have ever impressed me so powerfully (Mikkelson, 1994)
This is a rare phenomenon. Captain Mikkelson has been a seaman for over twenty years and has only viewed this one lunar rainbow; moreover, he has spoken to numerous career seamen and none reported ever seeing such a magnificent sight.
Another essential component of the rainbow is drops of water. Again, water drops from sprinklers or the sprays emitted from waterfalls can produce a rainbow, but I will focus on water drops that fall from the sky. A raindrop is nature’s reflective mirror in the sky. The smooth, yet internally curved, surface of a raindrop can refract and reflect light. A typical raindrop is spherical in dimension and thus has a symmetrical effect on light. Lynds (1995) points out that the “purity” of the colors of the rainbow depends on the size of the raindrops. Large drops (diameters of a few millimeters) give bright rainbows with well defined colors; small droplets (diameters of about 0.01 mm) produce rainbows of overlapping colors that appear nearly white. When it rains, the droplets are never the same exact size and shape; thus, a rainbow occurs in a range of colors.
Sunlight slows and bends when it enters a raindrop. Some of the light strikes the back of the drop at such an angle that it is reflected within the drop, this is the critical angle of 48º. Any angle greater than this and the light bounces off the back of the raindrop and is internally reflected towards our eyes. Each light ray bends differently from the others, so each angle is slightly different; therefore, the light is dispersed into a spectrum of colors from red, angle of 42º, to violet, angle of 40º. This is how a sundry of raindrops produce the dazzling colors of a rainbow (Ahrens, 1998).
Rainbows never form a full circle or any segment greater than a semicircle. At sunset and sunrise, the circle is smallest and the segment largest: as the sun rises higher the circle is larger and the segment smaller. Lynds (1995) explains:
“We do not see a full circle because the earth gets in the way. The lower the sun is to the horizon, the more of the circle we see -right at sunset; we would see a full semicircle of the rainbow with the top of the arch 42 degrees above the horizon. The higher the sun is in the sky, the smaller is the arch of the rainbow above the horizon.”
There are never more than two rainbows at one time. Each of them have three primary colors that blend and make the full visible spectrum of the rainbow. The colors are the same in both and their number and relation, but in the outer rainbow they are fainter and their position is reversed. In the inner rainbow the first and largest band is red; in the outer rainbow the band that is nearest to this one and smallest is of the same color: the other bands correspond on the same principle. 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. When sight becomes strained to a great distance, the appearance of the distant object is affected; it appears fainter; additionally, everything at a distance looks blacker, because sight does not reach it. The secondary, outer, rainbow is further away and less of it reaches the sun, so the reflection from the outer rainbow is weaker. This is why three rainbows or more would not be observed, because even the second is fainter, so that the third reflection would not have enough strength and would not reach the sun.
The order of the secondary rainbow is reversed because more reflection reaches the sun from the smaller, inner band. Because the band that is nearest the primary, inner, will reflect and result in the same color band of the secondary rainbow. Now the smallest band in the outer rainbow is that which is nearest, and so it will be red; and the second and the third will follow the same principle (Aristotle, 350 BC).
In the shorter days after the autumn equinox there may be a rainbow at any time of the day, but in the longer days from the spring to the autumn equinox there cannot be a rainbow about midday. The reason for this is that when the sun is north of the equator the visible arcs of its course are all greater than a semicircle, and go on increasing, while the invisible arc is small, but when the sun is south of the equator the visible arc is small and the invisible arc great, and the farther the sun moves south of the equator the greater is the invisible arc (Webster, 1994). Rainbows are observed more frequently in the summer than the winter because 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 (Humphreys, 1929).
Proverbs about rainbows predicting future weather have been around for centuries. “Red sky at night, sailors delight. Red sky in the morning, sailor take warning”, “Rainbow at night, shepherd’s delight; Rainbow in morning, shepherds take warning.”, “If there be a rainbow in the eve, It will rain and leave; But if there be a rainbow in the morrow, it will neither lend nor borrow”, and “Rainbow to windward, foul fall the day; rainbow to leeward, damp runs away” (Humphreys, 1923). The reason these proverbs are seemingly logical when you consider the fact that to see a rainbow rain must be falling in part of sky, and the sun shining in the other (Ahrens, 1998). In addition, to see a rainbow, or red sky, an individual has to be facing the rain and have the sun at your back. When we view an evening rainbow, we are facing east and towards the rain shower. When we view a morning rainbow, we are facing west, consequently, also towards the rain shower. In middle latitudes, clouds and wind tend to travel from west to east. Therefore, it follows that the rain that is in the west, as it is in a morning rainbow, will make its way across the land, eventually reaching our point of observation.
Ahrens,D. C., (1998). Essentials of meteorology (2nd ed.). Belmont, CA: West Publishing House
Aristotle, (350 B.C.E.), Meteorology (Translated by E. W. Webster, 1994). [On-line]. Available: http://www.
Humphreys, W. J., (1929). Physics of the air. Europe: McGraw-Hill Book Co.
Humphreys, W. J., (1923). Weather proverbs and paradoxes. Williams and Wilkins Company.
Lynds, B. T., (1995, September 19). About rainbows. [On-line]. Available: http://www.unidata.ucar.edu/staff/blynds/rnbw.html.
Mikkelson, V. E., (1994). Unexpected Beauty. [On-line]. Available: http://www.unidata.ucar.edu/staff/blynds/Mikkelson.html