The myths of the rainbow

While travelling one morning, I noticed some light rain and the sun shining brightly behind me: perfect conditions for a rainbow to form. So, I peered out the window of my bus. Sure enough, a brilliant band of colours arched across the sky. I was delighted to see such a rare occurrence in the morning, no less! Unfortunately, I had no idea what this portended.

"Rainbow in the morning, sailors take warning. Rainbow at night, a sailors delight." ¹

I would not have delighted so soon if I had known about this proverb. The rainbow soon disappeared, and bucketloads of rain followed.

Rainbows have always captivated us throughout history and have been the subject of folklore and physics alike. ² What is a rainbow though? Is it simply a trick of the light? Yes, and it is a fascinating one.

You need three things to see a rainbow: the sun, rain, and yourself, the observer. The sun is our light source, sending us white light, the entire electromagnetic spectrum. The wavelengths of light responsible for the rainbow are those in the visible range, between 380 - 700 nm. ³ When the light hits the surface of a raindrop at the correct angle, it bends. This is known as refraction and occurs because water is denser than air and slows light down. ⁴

The bending effect occurs due to light approaching at an angle, where one side slows down before the other, causing the rest of the wave to bend towards the shorter side. Shorter wavelengths are slowed more and so refract at a greater angle. This causes the white light to be separated as different wavelengths are refracted at different angles. The light then reflects off the back of the raindrop and refracts once more before reaching your eyes. ⁵

However, you can only see the colour of light approaching at the correct angle to your eye. For red, since it refracts at smaller angles, the angle between the incident light and our eyes is 42°. For violet, this angle is 40°. We need a large patch of rain to see the whole rainbow. ⁷

A rainbow is also a three-dimensional object. Any incident light that is between 40 – 42° to our eyes will allow us to see a rainbow. This forms a cone with our eyes at the apex, and the rainbow appearing at the rim. This means the rainbow is not a bow but a halo. Usually, we cannot see the other half of the rainbow since the ground blocks it. Unfortunately, this also means there is no gold at the end of the rainbow because the rainbow never really ends.

Back to my unfortunate morning, I should have known that the rainbow was not good news. Weather typically moves from West to East in Australia. Since the sun rises in the East, I would be facing West to see a rainbow in the morning, with the sun behind me and rain in front of me. Rain that was moving from West to East, directly towards me.

Article written by PhD student, Yuqing Li.