Is a rainbow parabolic? Why or why not?

optics visible-light reflection

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Rainbows are circular. They are formed by refraction and reflection of sunlight off of water droplets. This effect is strongest at 42 degrees, so the main rainbow consists of light 42 degrees from the point in the sky opposite the sun. This point is generally below the horizon, so we only see the top part of the circle, making it look like an arc rather than a circle.

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Eric Zhang

Knowledgeable in physics and math, not much else

Updated on May 01, 2020

Comments

Eric Zhang about 3 years

Recently, I heard that all projectiles form trajectories that are parabolic. That got me thinking about other arcs. My question is, are rainbows parabolic, hyperbolic, circular, elliptical, what shape do they make and how can we prove it?
- rob about 5 years
  
  From high enough above the water droplets whose reflections form the rainbow, it's sometimes possible to see the entire circle.
S. McGrew about 5 years

You could prove it to your satisfaction by carrying a paper plate around with you when there is likely to be a rainbow. When you see a nice full rainbow, hold the paper plate out away from you just far enough that with one eye closed you see the edge of the plate lined up with one of the color bands of the rainbow. As long as the plate axis is along your line of sight (so the plate is in a horizontal plane perpendicualr to your line of sight) you will see that the edge lines up perfectly with the color band in the rainbow.
probably_someone about 5 years

@S.McGrew Assuming that "horizontal" adopts its usual meaning of "parallel to the ground," there is no horizontal plane that is perpendicular to your line of sight unless you're looking directly upward.
S. McGrew about 5 years

Didn't mean to write that! I meant to say "vertical plane". Thanks for pointing it out.
probably_someone about 5 years

@S.McGrew Also, is a paper plate held at arms' length really the same angular diameter as a rainbow? That's a remarkable coincidence if true.
S. McGrew about 5 years

If I'd said "arm's length" I would thank you for that correction too-- but fortunately I only said to hold the plate out "just far enough..", which does work.