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Understanding the Science of Rainbows

What is a rainbow?

Everyone loves a rainbow! Even the grumpiest person cannot fail to feel lifted when they see this magical splash of colors in the sky.

Rainbows are a meteorological and optical phenomenon and have inspired, mystified and awed people across the world for thousands of years. Even though we now know its scientific explanation, the rainbow never fails to lift a heart and cause people to pause in wonder.

This page looks at the scientific reasons for why a rainbow occurs, how a rainbow is formed and the various characteristics a rainbow can have.

Table of Contents

When will you see a rainbow?

For a rainbow to occur there needs to be three things:

1. You need the sun to be shining behind you.

2. There needs to be a rain cloud or moisture in the air in front of you.

3. The sun must be shining through the rain cloud at an anti solar point of 42 degrees. An anti solar point is where the shadow of your head is, directly away from the sun.

Look at this photo below....

Can you see the people sitting on the bench? They have the sun shining behind them. You can see there's rain in the cloud in front of them. The sunlight is shining through millions and millions of tiny water drops, and as it does this the light refracts and disperses to show a beautiful spectrum of colors. Read on to find out how and why this happens!

You will see a rainbow at an anti-solar point of 42 degrees

The colors of the rainbow

Why do we always see the same colors in a rainbow in the same order?

Humans see light as white, but it is actually made up of many colors that we can't see because light moves so fast.

When the beam of sunlight passes through the water droplet it slows down and spreads out, separating each color that makes up white light into a spectrum of colors. This is called "dispersion". The colors of a rainbow are always seen in this order:


There are other many other colors, but we can't see them through our human eyes - like infrared and ultraviolet!

Each color in light is measured in wavelengths - some travel on longer wavelengths than others. Red, for example, is on a longer wavelength than violet. Red bends and changes direction when it travels through the water droplet much less than violet does. The index of refraction is the measure of speed of the wavelengths of color. You will see the colors of the rainbow in this same particular order because of the index of refraction.

If you want to learn more about the mathematics of rainbows , read this excellent guide The Calculus of Rainbows

You can see how light is dispersed through a raindrop by experimenting with a glass prism....see this video

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Light refracting through a prism

Why Rainbows are an arc - understanding light refraction

As the light travels through the water drop and disperses, it also does something called refraction.

Refraction is what happens to the light when it hits the water drop, it changes speed and bends. You can see this happening in the photo here of the glass prism on the right, refraction is happening as the white light (left) bends and disperses through the droplet.

So the reason why rainbows are an arc is because of the bending of and dispersing of light through millions of water droplets.

A more in depth article about refraction can be found here: "Snell's Law of the Refraction of Light."

The discovery of why rainbows happen

Rene Descartes (1596 - 1650) was a famous philosopher who came up with the modern theory for how rainbows occur in 1637. He was the first person to make the relation between round water drops and the interaction of refracting light. This is his sketch for how primary and secondary rainbows are formed.

A primary rainbow

Primary and secondary rainbows and the anti solar point

Primary rainbows shows red as the color on the outside, leading through to violet on the inside. You will see a primary rainbow at an anti solar point of 42 degrees. An anti solar point is the shadow of your head, directly away from the sun. In the photo above you can see the primary rainbow very clearly.

Secondary rainbows occur when the water droplets in the primary rainbow reflect light twice. Because it is the reflection of the primary, the colors are reversed. The colors are not so clear in the secondary and it is generally fuzzier and flatter than the primary. This rainbow occurs at 51 degrees from your anti solar point. Take a look at the image below, this shows both primary and secondary rainbows clearly.

Double rainbows showing primary and secondary bows

Characteristics of rainbows - Alexander's dark band

Alexander's Dark Band is the name for the dark sky between the primary and secondary rainbows you can see it really clearly in the photo above. It was named by Alexander of Aphrodisias, a Greek Philosopher who first noticed these optical phenomena in 200AD.