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Why do rainbows appear to have a fixed structure when a bunch of raindrops are 1. moving, and 2. granular?

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In short, this is because the location of a rainbow is not dependent on water droplets. The location is only dependent on the location of the Sun and of your eyes. The visibility of the rainbow is what depends on the presence of condensed water.

As each drop passes through a location that corresponds to that of the rainbow your eye will see the reflected photons originating at the Sun. Before and after the rainbow, that individual drop is not in a location that allows you to see these reflected photons. The rainbow appears stationary because it is (as long as you aren't moving) and droplets are falling through it often enough that it always appears visible.

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Ill update this later with some diagrams of the geometry of rainbows. – casey Aug 18 '14 at 0:38
Droplets aren't falling through the rainbow, they are the rainbow! :) Cheers. – Balinus Aug 20 '14 at 15:49

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