Diagram of light entering and leaving a droplet of water after it bounces off the back side of the droplet, from here: https://en.wikipedia.org/wiki/Rainbow#/media/File:Raindrop_optics.jpg

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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Monday, 16-Sep-2024 02:38:16 JST John Carlos Baez

   @JeremyMallin asked a fun question:

   "Does the fact that we have a nitrogen atmosphere with a fair amount of oxygen influence the appearance of rainbows here on Earth? Would rainbows in other atmospheres appear different in any way? Or is the medium in which they appear completely irrelevant?"

   The atmosphere doesn't matter much for the look of rainbows! But the liquid in the raindrops affects the 𝑠𝑖𝑧𝑒 of a rainbow.

   Here on Earth a rainbow makes a circle whose angular size is 42°. That is: if you look directly away from the sun, the rainbow will form part of a circle centered at that point, at an angle 42° away.

   But on Titan, where it rains liquid ethane, rainbows would be smaller, with an angular size of only 27° - at least if I did the calculation right!

   Why?

   Rainbows are created by the refraction of light as it moves between the air and the liquid in the raindrop. So what matters is the index of refraction of air - which is almost 1 as long as the atmosphere is not very dense - and of the liquid in the raindrop - which depends a lot on what that liquid is.

   The index of refraction of water is about 1.33, and here Wikipedia shows how to use that to compute the angular size of a rainbow on Earth:

   https://en.wikipedia.org/wiki/Rainbow#Mathematical_derivation

   When I instead use index of refraction of liquid ethane, which is 1.25, I get an angular size of 27°. But I might have made a mistake. Can you verify it?