This question asks How to tell if fog is made out of water droplets or ice crystals?

I know that ice fog makes a rainbow where fog does not.

Ice crystals aside: How does the water droplet size determine the characteristics of a rainbow? When is a water droplet too small to make a rainbow?

  • $\begingroup$ I guess it must be a limit, buy it might be very small. Even the kind of sprinklers that produce a fine mist can generate rainbows: google.com/… $\endgroup$ – Camilo Rada Mar 14 '19 at 18:29
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    $\begingroup$ I'd think they would have to be so small that they cannot refract and reflect sunlight, which would imply they'd have to be smaller than half a wavelength of blue light. $\endgroup$ – BillDOe Mar 14 '19 at 18:43
  • $\begingroup$ @Muze, I think you have more chances to get an answer to this in Physics SE $\endgroup$ – Camilo Rada Mar 14 '19 at 18:49
  • $\begingroup$ this is answered here en.wikipedia.org/wiki/Fog_bow. $\endgroup$ – trond hansen Mar 14 '19 at 19:18
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    $\begingroup$ @CamiloRada earthscience.stackexchange.com/questions/16308/rainbow-dynamics $\endgroup$ – Muze the good Troll. Mar 14 '19 at 22:00

Some time ago I posted this answer about how rainbows are formed, and the Wikipedia link Trond Hansen posted mentions droplet size relative to the wavelength of light.

For a rainbow to form, the droplet size has to be large enough, relative to the color with the longest wavelength of visible light, for it to be refracted before reflecting off the backside of the droplet. Refraction occurs because, as the wavefront encounters the change in density between air and water, it slows down. This implies that a droplet would have to be greater than half the wavelength of red light, which is about 740 nm, or about 370 nm.1 Also, the light responsible for producing the rainbow enters the droplet off-center and reflects off of the backside of the droplet off-center, so the droplet's diameter would need to be a bit larger than 740 nm.

  1. https://en.wikipedia.org/wiki/Light
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    $\begingroup$ Why larger the the shortest wavelength and not larger than longer one? How would a 420 nm droplet would be able to refract red light to produce a full rainbow, if the wavelength of red light is larger than the droplet? $\endgroup$ – Camilo Rada Mar 14 '19 at 21:35
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    $\begingroup$ @CamiloRada, oh...you're right. It would need to be the size of the longest wavelength, not the shortest. I will revise my response accordingly. Thanks. $\endgroup$ – BillDOe Mar 15 '19 at 20:50

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