Rainbow, the Colourful Arch

(A Scientific Perspective)

(written by: Willy Yanto Wijaya)

In a drizzling day, sometimes we can see a colourful arch decorating the sky. We call it rainbow, an arch consisting of colours: red, orange, yellow, green, blue, indigo, and purple. For a long time, rainbow has been highly praised and admired for its beauty. It has also been the source of inspiration for the human arts, cultures, even old mythologies.

As a matter of fact, many aspects of rainbow can be discussed to give us more understanding of this beautiful phenomenon. In this writing, we shall explore about what actually a rainbow is; how it happens according to scientific explanations; as well as various kinds of rainbow.

Simple general view considers a rainbow as a colourful arch in the horizon. Actually in many ancient beliefs, a rainbow is often associated with a bridge connecting the earth and the sky. Several others believed rainbow as a home for gods, gods’ arrow, cessation of chaos or even as a symbol of love eternity. These beliefs lasted for centuries till the coming of scientific explanations that give us new paradigm of understanding about the rainbow.

Donald Ahrens in Meteorology Today describes a rainbow as a light show caused by the spreading out of sunlight into its spectrums of colours and then diverted to the eye of the observer by water droplets. In other words, science currently explains a rainbow as an optical and meteorological phenomenon that causes a nearly continuous spectrum of light to appear in the sky when the Sun shines onto droplets of moisture in the Earth’s atmosphere. The rainbow takes the form of a multi-coloured arc, with red on the outside and violet on the inside. Traditionally, the full sequence of colours is most commonly cited as red, orange, yellow, green, blue, indigo, and violet. It is interesting then to know how this optical phenomenon happens and why it can be so colourful.

The formation of rainbow is an exciting problem in optics that was first clearly discussed by Rene Descartes in 1637. He examined the size of water drops, angle of the ray path and several physical parameters. After that, he constructed empirical laws that were very helpful as basics of contemporary explanations. We now understand that the rainbow’s appearance is caused by dispersion of sunlight as it is refracted by (approximately spherical) raindrops. The light is first refracted as it enters the surface of the raindrop, reflected off the back of the drop, and again refracted as it leaves the drop. The overall effect is that the incoming light is reflected back over a wide range of angles, with the most intense light at an angle of about 40°–42°, regardless of the size of the drop.

The traditional diagram to illustrate this is shown here as adapted from Humphreys, Physics of the Air.

The diagram represents the path of one light ray incident on a water droplet from the direction SA. As the light beam enters the surface of the drop at A, it is bent (refracted) a little and strikes the inside wall of the drop at B, where it is reflected back to C. As it emerges from the drop it is refracted (bent) again into the direction CE. The angle D represents a measure of the deviation of the emergent ray from its original direction. Rene Descartes calculated this deviation for a ray of red light to be about 180 – 42 or 138 degrees. That’s why the form of a rainbow is an arch and why the position of the rainbow in the sky is always in the opposite direction of the Sun with respect to the observer.

Next to wonder is why a rainbow is so colourful. The traditional description of the rainbow is that it is made up of seven colours – red, orange, yellow, green, blue, indigo, and violet. Actually, the rainbow is a whole continuum of colours from red to violet and even beyond the colours that the eye can see. The colours of the rainbow arise from two basic facts.

First, sunlight is made up of the whole range of colours that the eye can detect. The range of sunlight colours, when combined, looks white to the eye. This property of sunlight was first demonstrated by Sir Isaac Newton in 1666. Second, light of different colours 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 colours because blue light is bent or refracted more than the red light.

This implies that when we see a rainbow and its band of colours 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 colours would have a width of almost 2 degrees. 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.

Observations conducted until now has revealed many kinds and variants of rainbows. There are reflection rainbows, lunar rainbows, secondary or double rainbows, triple and even supernumerary rainbows.

A reflection rainbow is defined as one produced by the reflection of the source of incident light (usually the sun). The reflected rainbow may be considered as a combination of two rainbows produced by sunlight coming from two different directions-one directly from the sun, the other from the reflected image of the sun. The angles are quite different and therefore the elevation of the rainbow arcs will be correspondingly different.

Besides by the sunlight, rainbow can also be produced by the moonlight. A full moon is bright enough to have its light refracted by raindrops just as is the case for the Sun. Moonlight is much fainter, of course, so the lunar rainbow is not nearly as bright as one produced by sunlight. Lunar rainbows are very rare and have infrequently been observed even since the time of Aristotle or before.

Occasionally, outside a primary rainbow, there happens a second, dimmer rainbow. This is called secondary or double rainbow. Secondary rainbows are caused by a double reflection of sunlight inside the raindrops, and appear at an angle of 50°–53°. As a result of the second reflection, the colours of a secondary rainbow are inverted compared to the primary bow, with blue on the outside and red on the inside.

A triple, or third, rainbow can be seen on rare occasions. In some cases, even a few observers have reported seeing quadruple rainbows in which a dim outermost arc had a rippling and pulsating appearance. These rainbows would appear on the same side of the sky as the Sun, making them hard to spot.

Another beautiful and striking rainbow phenomenon can be observed, consisting of several faint rainbows on the inner side of the primary rainbow, and very rarely also outside the secondary rainbow. They are slightly detached and have pastel colour bands that do not fit the usual pattern. They are known as supernumerary rainbows.

In conclusion, a rainbow is an optical and meteorological phenomenon that causes a nearly continuous spectrum of light to appear in the sky that happens when the Sun shines onto droplets of moisture in the Earth’s atmosphere and that has many kinds and variants of appearance.

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