Why are rainbows curved?

Why are rainbows curved?

Most people are familiar with the idea that rainbows are a result of sunlight refracting through water droplets in a rain cloud. The observant may have noticed that the sun is usually close to the horizon and behind you when a rainbow appears. But why are they always curved? It’s due to the angle that the light rays are refracted off the water droplets. The light is refracted in any direction by an angle of 40-42 degrees (depending on the wavelength or colour) due to the shape of the water droplet and the fact that its water. So only a small fraction of the light will be refracted back towards you, but as a rain cloud contains billions of water droplets that is still enough light to see the rainbow. To understand how the curve is formed, hold your arm out in front of you and trace out a circle keeping your arm at an angle of 40 degrees to the horizontal. The refracted light follows a path as though it were travelling from the tip of your hand to the top of your arm. The constant angle of refraction creates the arc we see in the sky. We only see a section of the circle, because the horizon blocks out the rest.