According to Ahrens (1998), a rainbow is an awe-inspiring phenomenon produced by our atmosphere, often regarded as one of the most captivating exhibitions of light on Earth. The perception of a rainbow varies for each individual, resulting in a distinct and individualized encounter. As Humphreys underscores:
According to Humphreys (1929), the distribution of colors in a rainbow is unique to each observer’s perspective, resulting in different rainbows being seen by different people.
Lynds (1995) states that a camera lens has the ability to capture and display an image of a rainbow, which can be observed by multiple people.
The rainbow consists of seven vibrant colors – red, orange, yellow, green, blue, indigo, and violet. It also includes additional colors that are not visible to the human eye. Artists cannot accurately reproduce the colors of the rainbow because they arise from mixing and no combination can create red, green or purple which are unique to the rainbow (Aristotle, 350 BC). Understanding this fascinating phenomenon requires knowledge of physics and mathematics. Light and water droplets play a crucial role as they interact and move according to complex laws of nature. Moreover, specific conditions must be met for a rainbow to appear.
The formation of a rainbow requires the presence of light. While it is possible to create an artificial rainbow using artificial light, my paper will focus on naturally occurring rainbows produced by natural light. The sun is the primary source of natural light that creates rainbows. However, there are rare instances when a lunar rainbow can be formed using moonlight. Witnessing a lunar rainbow requires specific conditions to be met. Firstly, the moon must be in its full phase which happens once a month. The light emitted by a full moon is relatively faint, resulting in a less prominent lunar rainbow compared to a solar rainbow. Additionally, the full moon must either be rising or setting. A naval officer named V.E. Mikkelson shared his reaction upon realizing that the spotlight he observed was actually a lunar rainbow.
The unusual sight I observed was a rainbow caused by moonlight. It was created by moonlight piercing through rain that fell from a fluffy cumulus cloud. The rainbow contained the usual colors, but they appeared fainter and less vivid compared to those produced by direct sunlight. They were reminiscent of pastel colors. I felt completely captivated by this spectacle. Despite having witnessed numerous natural wonders, I have never been as profoundly impressed as I was on this occasion (Mikkelson, 1994).
This is an extraordinary occurrence. Captain Mikkelson, who has been a seaman for more than two decades, has witnessed only this single lunar rainbow. Furthermore, he has conversed with several experienced seamen, and none of them have ever encountered such a splendid spectacle.
Water drops are an important part of the rainbow. While sprays from sprinklers or waterfalls can create a rainbow, I will focus on raindrops. Raindrops act as mirrors in the sky, reflecting and refracting light. They have a symmetrical effect on light due to their spherical shape. The size of the raindrop determines the purity of the rainbow’s colors. Larger drops create bright rainbows with distinct colors, while smaller droplets produce overlapping colors that appear almost white. Since raindrops vary in size and shape, a rainbow displays a range of colors during rainfall.
When sunlight enters a raindrop, it is slowed and bent. Some of the light is reflected within the drop if it strikes the back of the drop at an angle greater than 48º, known as the critical angle. Light rays with angles greater than the critical angle bounce off the back of the raindrop and are internally reflected towards our eyes. Each light ray bends differently, resulting in a dispersion of colors ranging from red at an angle of 42º to violet at an angle of 40º. The combination of these dispersed colors from multiple raindrops creates the vibrant colors of a rainbow (Ahrens, 1998).
According to Lynds (1995), rainbows only appear as semicircles or smaller segments, never forming a complete circle. The size of the circle is smallest during sunset and sunrise, while the segment is largest during these times. As the sun reaches higher points in the sky, the circle becomes larger and the segment becomes smaller.
Due to the earth blocking our view, we are unable to see the entire circle of the rainbow. Nonetheless, as the sun moves closer to the horizon, more of the rainbow’s circle becomes visible. At sunset, a semi-circle of the rainbow is observable with its top arch positioned 42 degrees above the horizon. Conversely, when the sun is higher in the sky, the arch of the rainbow above the horizon appears diminished.
At any given time, there can be a maximum of two rainbows. These rainbows have the same colors and order, but their positions are reversed and the outer rainbow is fainter. The inner rainbow has its largest band in red, while the outer rainbow has its closest and smallest band also in red. The other bands follow this pattern as well. The primary rainbow occurs from one internal reflection, while the secondary rainbow happens when there are two internal reflections. When objects are seen from a great distance, they appear darker and fainter due to strained sight. The secondary rainbow is located further away and receives less sunlight, which causes it to have a weaker reflection. This explains why we only observe up to two rainbows; even the second one is fainter and unable to reflect back enough light towards the sun.
Aristotle explains that the secondary rainbow has a reversed order due to more reflection reaching the sun from its smaller, inner band. Thus, the band closest to the primary, inner rainbow will reflect and produce the same color band in the secondary rainbow. In contrast, the outer rainbow starts with a red band nearest to it, followed by subsequent bands following this principle (Aristotle, 350 BC).
Rainbows can be seen at any time of day during the shorter days after the autumn equinox, but they cannot be seen around midday during the longer days from spring to the autumn equinox. This is due to the sun’s position in relation to the equator. When the sun is north of the equator, its visible course arcs are greater than a semicircle and continue to increase, while its invisible arc is small. Conversely, when the sun is south of the equator, its visible arc is small and its invisible arc is large. As the sun moves farther south of the equator, its invisible arc becomes even greater (Webster, 1994).
In summer compared to winter, rainbows are more commonly observed because rainfall and sunshine are necessary for their formation. In winter, water droplets freeze into ice particles that cannot create rainbows. However, these ice particles scatter light in other interesting patterns (Humphreys, 1929).
Throughout history, there have been various proverbs that predict weather based on the presence of rainbows. Some well-known examples include “Red sky at night, sailor’s delight. Red sky in the morning, sailor take warning”, “Rainbow at night, shepherd’s delight. Rainbow in morning, shepherds take warning”, “If there is a rainbow in the evening, it will rain and then clear up; but if there is a rainbow in the morning, it will neither borrow nor lend” and “Rainbow to windward, foul fall the day; rainbow to leeward, damp runs away” (Humphreys, 1923). These sayings make sense because a rainbow can only appear when it is raining in one part of the sky while sunlight shines through another (Ahrens, 1998). Furthermore, observing a rainbow or red sky requires facing towards the rain with sunlight coming from behind. An evening rainbow means we are looking eastward where rainfall occurs. On the other hand, a morning rainbow implies facing west towards rainfall as well. In middle latitudes where clouds and wind usually move from west to east, it follows that rain from the west seen in a morning rainbow will eventually reach our location as it moves across land.
Bibliography
According to Ahrens (1998), the book titled “Essentials of Meteorology” is in its 2nd edition and was published by West Publishing House in Belmont, CA.
Aristotle’s Meteorology, translated by E. W. Webster in 1994, is available online at http://www.
The link to “classics.mit.edu/Aristotle/meteorology.3.iii.htm” is written within a paragraph tag.
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 at: http://www.unidata.ucar.edu/staff/blynds/rnbw.html.
The source “Unexpected Beauty” by Mikkelson (1994) is available online at http://www.unidata.ucar.edu/staff/blynds/Mikkelson.html.
