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tsuuga t1_je3i3y6 wrote

Third and fourth order rainbows can happen. They're just very faint and occur near the sun.

Light reflects off the inside of water droplets at a 40-42.5 degree angle (depending on wavelength), so the primary and secondary rainbow, reflecting at less than 90 degrees, appear on the side of the sky opposite the sun. The third and fourth rainbow, at ~120 and ~160 degrees, appear close to the sun, and are thus difficult to see.

Here's a scientific paper from somebody who managed to get a photograph of a triple rainbow.

and a quadruple

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WhyteBeard OP t1_je3ib88 wrote

Oh wow, thanks for the answer! So there are third and fourth order bows predicted mathematically but are not visible to the naked eye and we won’t ever see a third bow opposite the sun like a regular single or double rainbow.

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