Rain bows form in full circles!

Q: Why are rainbows always in a semi-circle shape?

Krishna: Rainbows are circular!

Rainbows form when the sun's rays pass through millions of drops of water – that's why we normally see them around shower clouds. A raindrop acts like a prism, splitting "white" light from the sun into its seven component colours, the colours of the rainbow.

Light travels at different speeds in air and water. As the sun's rays pass through a water droplet, they are slowed down and this causes them to bend, a process called refraction. 

Because a rain droplet is round, the light passing through follows its circular shape. All rainbows are actually full circles, but most people only ever see an arc or semicircle because they are standing on the ground and the other half is cut off by the horizon.

A rainbow is the diffraction of sunlight through water droplets in the air. To see a rainbow, you need to be looking at light rain with the sun behind you. The rainbow is curved as it reflects the round shape of the sun. It is a semicircle because only half of your field of vision is the air (the other half is the Earth).

If  you are high enough, for instance, if you see a rainbow from an aeroplane, you might see the full circle.  If you are in an aeroplane with the sun directly overhead and you look down into a raincloud, you will see the rainbow is a full circle, again reflecting the fact the sun is round.

Rainbows are circular because raindrops are spherical. When light from the Sun enters a raindrop it is largely reflected back inside a cone with a half-angle of 42 degrees. The reflected light is strongest along the surface of this cone where it is broken up into a spectrum of colours. When we see a rainbow we are looking at those drops from which the light along the surface of the cone enters our eyes. Consequently, a line from the Sun through our head passes through the centre of the circular rainbow. The angle between this line and any point on the rainbow is about 42 degrees.