From the ground only the top part of the resulting rainbow is visible, the one in the shape of a multicolored arc. However, if we rise above the surface of the Earth we will realize that a rainbow continues below the horizon. That is why from the air we have a greater chance of witnessing a truly amazing phenomenon, a complete circular rainbow. This 360-degree rainbow was photographed from a helicopter flying, between a downpour that produced it and the rays of the Sun, over Cottesloe Beach, in Perth, Australia.
Historical conception of the rainbow
Throughout history and at different points in geography, an attempt has been made to explain the appearance of the rainbow in different ways. He could not give a scientific explanation because there was no scientific method as we know it today but at least they gave fantastic explanations.
Illustration of the worlds according to Norse mythology with the Bifrost
Irish mythology
Without a doubt, the most "fantastic" and well-known conception he has of rainbows is that of the existence of a kind of gnome with a cauldron.
According to Irish mythology, leprechauns are a species of gnomes that carry a pot full of gold. They are defined as cunning and greedy, and that is why the story goes that to protect their treasure they only come out of hiding when a rainbow appears.
Leprechaun with a pot of gold at the base of a rainbow
The children were told that if they were able to reach the point on earth from which the rainbow came out, they would meet one of these beings and be able to keep the gold.
And, when we see a rainbow it gives us the feeling that it is like a colored ray that starts from a point on earth, as if someone were projecting it into the sky. The thing is, the rainbow is "generated" in our eyes (It is an optical effect), and whatever we walk we will never reach its base. (We will see later why).
Newton's prism
Optics was the object of study of many civilizations and as the years passed, advances in this branch of physics progressed.
The study of the rainbow and the colors belongs to this branch, and it was not until approximately 1670 when Isaac Newton formulated a theory that related the visible or white light and the colors of the visible spectrum.
Visible light is one of the bands of the electromagnetic spectrum, and within this band the colors appear, arranged in the same way as in the rainbow. The less energetic electromagnetic waves go below red and are called infrared, while the most energetic waves that go after violet are called ultraviolet.
Newton's experiment
Before Newton, Descartes already suspected the idea of decomposing light into colors. However, he was not able to obtain more than two colors and did not know why it happened.
To study the behavior of light Newton used a pair of glass prisms. In a darkened room where only a beam of light entered, he placed a prism in front of the beam, so that it passed through it and reflected the light on the opposite wall. He observed that the colors of the rainbow appeared on the wall in order one after another.
Newton in his workshop with the prism experiment
However, at this point there were two possibilities; Either the prism gave color to the light, or the light was the mixture of all the colors and the prism simply decomposed it.
In order to reach a conclusion he realized in a second prism that he placed behind the light decomposed into colors. After moving the prism through each of the colors
Furthermore, by meticulously placing a second prism he was able to mix all the colors and project a beam of white light.
Two connected Newton prisms that decompose and unite colors
Newton showed that what is normally known as visible or white light is really an indistinguishable union of waves of different frequencies, each associated with a color that our eye is capable of perceiving.
How does Newton's prism work?
The explanation is quite simple and is due to the difference in frequency of each of the colors + the refraction due to the change of medium.
Refraction is the change in direction and speed that a wave experiences when passing from one medium to another with a different refractive index.
Refraction of light in water
This deviation in the direction of propagation is explained by means of Snell's law. On the other hand, and what really matters to us, is that the speed of penetration of light in a medium other than vacuum is related to the frequency of the wave.
For a ray of light with an angle of incidence {\ displaystyle \ scriptstyle {\ theta _ {1}}} in the first medium, angle between the normal to the surface and the direction of propagation of the ray, we will have that the ray propagates in the second medium with an angle of refraction {\ displaystyle \ scriptstyle {\ theta _ {2}}} whose value is obtained by means of Snell's law:
{\ Displaystyle n_ {1} \ \ operatorname {sin} \ theta_ {1} = n_ {2} \ \ operatorname {sin} \ theta_ {2} \,}
Where {\ displaystyle n = \ frac {c} {v}} \ is the refractive index, which depends on the speed v of the wave in the medium.
Snell's Law
When a beam of white light passes from one medium to another, each color undergoes a slight deviation because each has a certain frequency. This phenomenon is known as light scattering.
Newton's prism decomposing colors
Formation of a rainbow
The manifestation of the rainbow, as we have explained with Newton's prism, is due to a decomposition of white light into pure colors.
Indeed, the drops of water that are still in the environment. That is why a rainbow only appears after it has rained a lot (Environment very loaded with drops of water) or there is a slight drizzle (Drops are falling but they do not reduce visibility or cover the sun).
To understand the formation of the rainbow and understand why we will never be able to reach its base, it is necessary to be very clear that the rainbow is generated in our eye. It is an optical effect that depends on the observer due to the incidence of the rays. Nothing to do with an aurora borealis for example, where what you see are particles that exist as such.
Animation of an aurora borealis
The rainbow is generated in such a position that when we see it just behind us, the sun is located. The thing is, the sun's rays advance and enter the drops of water, producing refraction (the colors separate) and reflection (The ray returns to us).
Refraction of light in water droplets
What happens is that this ray with a circular shape due to its geometry goes directly to our eyes, and that is why from the earth we see the half circle or rainbow.
Graphic formation of a rainbow
Full rainbow of circular shape from an airplane
View of a full rainbow from the sky
It is a bit what happens with mirages, also caused by the refraction of hot air on the surface. THERE IS NOTHING there, it is an optical effect that is generated in our mind.
