Why is the rainbow shaped like an arc (and not a straight line)?

Oxymorons also exist in nature, because in the midst of the storm there is room for light. When Mother Earth decides to surprise us, she can offer us one of the most interesting scenarios; in the background the rain that falls with great intensity and behind it the sun brighter than ever. The result of such contrast is a rainbow that appears in the middle of the union of two scenarios that seem contrary. But beyond the beauty of this phenomenon, questions come to mind about why it originates and why it is shaped like an arc and not a straight line. To answer these questions we will have to delve into history.

Newton’s experiment

In 1667, one of the greatest minds that ever existed in humanity, presented to the Royal Society an experiment that would forever change the perception of light. Through a small inlet of light reflected on a glass prism, he discovered a fundamental law of nature and wrote it down in Latin:

“Nec variat lux fracta colerem”, (refracted light does not change color).

The experiment, which today is considered one of the most important in the history of science, taught Newton two basic ideas about light. The first is that white light is composed of multiple colors that in combination make us observe the characteristic color of light. The second discovery is that the colors into which white light is decomposed are immutable. That is, no matter how many times and what the conditions are, the prism experiment would always result in the same decomposition and order of colors.

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With this context in mind, we can deduce that the rainbow is the natural representation of Isaac Newton’s experiment, although the elements change in some way. Instead of a glass prism, nature uses raindrops to reflect and refract light from the sun. When light passes through the droplets, it breaks down, reflecting the seven colors we call the rainbow. But why does it have that peculiar shape of an arc and not a straight line? The answer is hidden in the small raindrops.

Why does the rainbow have that shape?

Often the representation of raindrops has a peculiar shape, with a pointed angle at the top and an oval base at the bottom. However, in real life they do not have such a shape, but are completely round. With this in mind, the next thing is to think about the rays coming from the sun passing through raindrops, the result is more or less the same as what Isaac Newton experimented more than three centuries ago. Light is broken down into the seven immutable colors that we call rainbows and reflects and refracts them, although the direction of the light that we observe changes a little.

When a ray of light reaches a drop and tries to pass through it to continue on its path, a small fraction fails and is reflected back. In that sense, a percentage of light that reaches the drops does not manage to pass through them and instead, is reflected from almost the same place where it tried to enter, although now decomposed into colors.

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However, the shape factor of the drop comes into play and due to the curvature of its walls, the direction of the light changes, making it curved as a result of reflecting and refracting between so many curved surfaces. The light shoots out in decomposition at an angle of 138º with respect to the incident light and it is precisely this angle that gives the rainbow its peculiar circular shape.

In fact, due to the characteristics of the planet that interrupts the path of light with the Earth’s surface, we can see the rainbow as a semicircle. But in places where there is no impediment in the path of light, the complete circumference can be seen. That is, the refraction of light does not stop and thanks to the curvature of the drops it is able to generate a completely circular projection. However, from our perspective it is not possible to observe it because the ground interrupts the circumference.

Although there are special cases where the genuine shape of the rainbow can be observed. For example, at the edge of a waterfall where sunlight passes through the drops that are ejected due to the fall. Thanks to the height, in the distance the complete circumference of the seven colors that make up white light will be observed.

This phenomenon is amazing and shows us the true nature of light. Now, every time you see a rainbow, think that you are looking at a natural replica of what Isaac Newton discovered more than three centuries ago and that it gives us the most beautiful views.

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