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Many explanations of the shape of rainbows as constant angle reflections do assume the light, incident on rain droplets, to be a parallel beam of light rays. That might for the sun-earth system be correct. But imagine the earth much closer to the sun and imagine that water would still exist as a fluid: The light rays are now divergent, i.e. position of the droplets in the sky w.r.t to sun and observer matters now for the incident angle on the droplets.

What will the shape of the rainbow be? will rainbows still be circular? or would they be flatter like a hyperbola?

Side question: why do all explanations of rainbow shape assume that a rainbow can only exist in a single narrow plane. (i.w. why has a rainbow no thickness in the direction of reflection )

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    $\begingroup$ Why would the rays entering the droplets not be parallel? $\endgroup$
    – joseph h
    Commented Jan 10, 2022 at 1:07
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    $\begingroup$ you can sometimes see a rainbow effect from a flashlight outside in cold night air with some water vapor $\endgroup$
    – antimony
    Commented Jan 10, 2022 at 2:42

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Tips: rainbow comes from both refracted and reflected light.

Side question first: In the case of a rainbow you are looking at an image that's created by the reflection of light (indeed it can only be seen on the opposite side of the sun, with the observer being at 42°). So it will always be a 2D image (like your image on a mirror). To be more clear, the droplets will act as a mirror.

With a set of non-parallel rays, you will just see a dimmer rainbow simply because there will be fewer rays reflected at the critical angle of 42° (that's the angle at which the light does a complete turnback within the water droplet). So most probably you will not be able to see the rainbow

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