What Makes a Rainbow?

In Nature, Physics by Mystifact

Rainbows are one of nature’s finest works of art. In medieval times, they were always linked to happiness and good luck. They were even implemented into religion, as a gift from God! However, in this day and age, we want to know the inner workings of them, which is what I am going to help you understand today.

How do Rainbows work?

To understand how Rainbows are formed we must first understand both the terms refraction, and dispersion.

What is Refraction?

Refraction is when light changes speed when it travels from one body (or medium) into another. When it enters a different medium of a different refractive index, the speed travelled in this new medium is different, meaning the light ray looks like it is changing direction.

Don’t be thrown off by the term ‘refractive index’. It is just a number given to any object which describes how fast light would travel through it. Generally, the higher the refractive index, the slower light travels through that medium [1].

You can test this out at home! Just put a pencil in a glass of water, and the pencil will look like it is cut in half at the point of contact with water. This is because the medium, air, has a lower refractive index than the medium, water; so light travels slower in this water giving the illusion that the pencil is snapped in half. This is due to the light rays travelling a different direction as explained above.

Figure 1: Pencil in cup of water experiment

Typically, light travels from the Sun to Earth in 8 minutes. If you were to put a massive body of water between them, it would take the light 11 minutes, as water has a higher refractive index. As explained above; this means light travels slower!

What is Dispersion?

White light is the mixture of all wavelengths of visible colour. Every colour has a certain property called a wavelength. When combined into a mixture, you get white light. Dispersion of light is when this mixture of wavelengths is split up by refraction [2]. The famous prism is capable of doing this, as shown below.

Figure 2: Image showing the dispersion of white light with a prism

Combing Dispersion and Refraction

Sunlight appears white to us. When this white light approaches a medium of higher refractive index, such as water; this white light slows down – but – since white light is a combination of all wavelengths of visible light, different wavelengths slow down more than others, which splits it up into its constituent colours. This splitting of light looks very much like a rainbow… but how does it form in the sky?

The formation of a Rainbow

By taking what we have learnt about refraction and dispersion and applying this knowledge to our new situation; let’s send a white beam of light through a droplet of water in the rain. Some of this light will refract into the water droplet, then reflect off the inside wall of the droplet, then refract back out into the air. Typically, the angle between the light approaching the water droplet and the light coming out of the droplet should be about 42 degrees for rainbows to be seen [3].

Figure 3: Image showing light entering the droplet of water and exiting at an angle of 42 degrees

This is the tough part. The situation we have discussed is for one droplet of water. When this droplet refracts, violet is at the top of the spectrum, which goes through to blue, green, yellow, orange then red (as shown in figure 3). This means that the first colour from the top of a rainbow should be violet, right? If you look at a rainbow you’ll find the top colour is red and the bottom is violet, meaning rainbows appear upside down. Why is this?

Imagine droplets of water high up in the sky. When the light refracts out of these droplets, the red light at the bottom of the spectrum reaches our eyes and the other lights travel above our heads. As light enters water droplets further down closer to the ground, red light begins to travel under our heads and different colours are now entering our eyes. Therefore, the spectrum of a rainbow seems to be upside down. The image below attempts to explain this.

Figure 4: Image showing how the rainbow appears to be upside down

Why isn’t there a rainbow every time it rains?

Here is the fun part. There is always a rainbow when it rains, but it depends on your location, whether you see it or not. Since the light is refracted at an angle of roughly 42 degrees (as mentioned before), it depends where you are on the ground such that the refracted light reaches your eyes.

This means everyone sees rainbows differently. Effectively, nature has painted you a beautiful landscape… exclusively, for you.

If you have any questions, leave them below and until next time, take care.

~ Mystifact

[1]: https://en.wikipedia.org/wiki/Refraction
[2]: https://www.merriam-webster.com/dictionary/dispersion
[3]: http://faculty.cord.edu/manning/physics215/studentpages/genamahlen.html

Please note; no copyright infringement is intended. All images used have been labelled for re-use on Google Images. If any artist or designer has any issues with any of the content used in this article, please don’t hesitate to contact me to correct the issue.

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Why does the road look like it’s WET on a hot day? The Physics behind a Mirage
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Previous articles:
Why Do We Dream?
Metal Detectors are MAGIC?
Are we alone in the Universe?

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