In 1665, Isaac Newton demonstrated that the Sun's light rays are made up of a multicoloured band of light by shining sunlight through a prism. The Sun may look yellow-ish when you look up at it in the sky, it actually emits white light! The refraction property of electromagnetic waves is why the white sunlight splits up into a 'rainbow' when passing through a prism – prior to this discovery, not much was known about the composition of sunlight or white light.

Red, orange, yellow, green, blue, indigo, and violet. Rainbows occur when we have sunlight interacting with water droplets. The water droplets can be thought of as mini prisms (like the one used in Newton's experiment). As sunlight passes through a particular droplet, there is a change in refractive index (refractive index tells you by what factor electromagnetic waves slow down in a particular medium), causing the light within it to reflect and refract. The way in which the light rays enter and leave the droplet is governed by Snell's law: n1sin(θ1)= n2sin(θ2). This equation can be applied at each droplet-air boundary to unravel the subsequent motion of the ray. Different wavelengths (corresponding to different colours) of light bend at different angles, causing the white light to separate into a spectrum. 

We need a bunch of droplets for a rainbow to fully form, as each droplet sends a different wavelength (colour) of light into your eyes. This typically happens on a rainy day, but can also happen near sprinklers, under waterfalls, and on misty days. Rainbows are actually completely circular in shape, but half of this circle lies below the horizon, which is why it appears as a semicircle! In addition, since we all observe a different set of droplets at different angles, the rainbow you observe will be entirely unique to you: where you see the rainbow is completely dependent on your current position.

Apologies for the dodgy diagram above – I found this in my camera roll from a few years ago! However, it's pretty accurate in describing the physics behind primary rainbows. Refraction occurs twice (at the boundaries) and reflection once within the raindrop. The reflection angle for red light is ~42 degrees, and ~40 degrees for blue light (as illustrated in the diagram). Therefore, primary rainbows can be seen 40-42 degrees up in the sky relative to the ground.

Sometimes, the light ray can reflect twice within the droplet before leaving it. This is why we may see a double rainbow 12 degrees above the first rainbow (52-54 degrees up in the sky relative to the ground). The secondary rainbow will always be fainter than the primary rainbow since only some of the light reflected twice will reach your eyes – there will be a higher likelihood of the light 'leaking' as it takes a longer trip inside the droplet. Additionally, the second rainbow will appear to be inverted with respect to the primary rainbow; red will be on the bottom, and violet will be on the top. This is because the secondary reflection acts as a mirror. 

In very rare cases, we can have 3 or 4 rainbows if more reflections occur within the droplets. We may also see overlapping colours within a rainbow – this is known as a 'supernumerary rainbow'. Supernumerary rainbows are caused by the interference of incoming light waves which overlap, as the crest of one wave lies on top of the trough of the other.

published: 21/05/23 by kaan evcimen