rainbow

July 3, 2023

Pavle Ignjatović

How and why do rainbows form?

Behind one of the most colorful events in nature stands nothing more than couple of physics laws, but some people still do not understand them completelly. If you are among them, I am sure that you will be able to explain this phenomenon in just a few minutes.

Let's remember some foreknowledge, first. We all know that for the formation of a rainbow sun and rain are needed, and that it will not form in the absence of either of them. So, formation has something to do with the light passing through water.
Because water is denser then air, light passing through raindrop slows down and changes direction, exiting at different angle. This is called refraction. Sunlight (which appears white to us) is made of different colors, each with its own wavelength, and slowing by different amounts. This leads to dispersion - process of separating white light to all colors of visible spectrum (red, orange, yellow, green, blue, indigo, and violet).
refraction

Refraction. Credits: https://www.metoffice.gov.uk/weather/learn-about/weather/optical-effects/rainbows/how-are-rainbows-formed

The image shows simplified process of dispersion - separating colors of visible spectrum from white light, with reflection being just light "bouncing" of the drop from the inside.

After this happens, when standing in the right place, an observer may see refracted and dispersed light, forming the rainbow. Arc's center stands in the antisolar point - point directly oppsite the sun. Different colours exit the droplets at angles that vary by around two degrees from red (with the longest wavelength, around 650 nanometers) to violet (with the shortest wavelength, around 400 nanometers), so red will be the first, and violet the last color on the rainbow. Ultrared and ultraviolet light can also be found in it, but human eye cannot register these wavelengths.

Interesting things to notice:
full rainbow

Circular rainbow. Credits: https://science.howstuffworks.com/nature/climate-weather/atmospheric/rainbows-are-circular.htm

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