<p>Some time ago I posted <a href="https://earthscience.stackexchange.com/questions/7480/what-causes-a-rainbow-its-colours-and-its-shape/7482#7482">this</a> answer about how rainbows are formed, and the Wikipedia link Trond Hansen posted mentions droplet size relative to the wavelength of light.</p>

<p>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.<sup>1</sup> 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.</p>

<hr>

<ol>
<li><a href="https://en.wikipedia.org/wiki/Light" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Light</a></li>
</ol>

CC BY-SA 4.0
2019-03-14T21:35:33.960Z
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?
Camilo Rada
CC BY-SA 4.0
2019-03-15T20:50:27.287Z
@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.
BillDOe
CC BY-SA 4.0
2024-08-14T04:16:19.253Z
The smallest size of a water droplet in a cloud is about 5 um. This is much larger than the wavelength of visible light. So why don't the water droplets in clouds produce rainbows, even when the sun is in the appropriate position?
Timothy Smith
CC BY-SA 4.0
2019-03-14T21:27:06.930Z
2019-03-15T20:55:19.290Z
2019-03-15T20:55:19.290Z
BillDOe
<p>This question asks <a href="https://earthscience.stackexchange.com/questions/13831/how-to-tell-if-fog-is-made-out-of-water-droplets-or-ice-crystals">How to tell if fog is made out of water droplets or ice crystals?</a> </p>

<p>I know that ice fog makes a rainbow where fog does not.</p>

<p>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?</p>

CC BY-SA 4.0
2019-03-14T18:29:19.190Z
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: https://www.google.com/search?biw=2400&bih=1150&tbm=isch&sa=1&ei=UJ2KXJOYG4uQ0PEPlvyS6AI&q=Sprinkler+rainbow&oq=Sprinkler+rainbow&gs_l=img.3..35i39j0i8i30l3.37218.37374..37672...0.0..0.57.110.2......1....1..gws-wiz-img.qUhOqpGA5gc
Camilo Rada
CC BY-SA 4.0
2019-03-14T18:43:12.920Z
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.
BillDOe
CC BY-SA 4.0
2019-03-14T18:49:56.863Z
@Muze, I think you have more chances to get an answer to this in Physics SE
Camilo Rada
CC BY-SA 4.0
2019-03-14T19:18:13.630Z
this is answered here https://en.wikipedia.org/wiki/Fog_bow.
trond hansen
CC BY-SA 4.0
2019-03-14T19:42:34.427Z
@BillDOe that is a start for a good answer.
Muze
CC BY-SA 4.0
2019-03-14T22:00:44.337Z
@CamiloRada https://earthscience.stackexchange.com/questions/16308/rainbow-dynamics
Muze
<water><light><fluid-dynamics><cloud-microphysics>
At what point are water droplets too small to make a rainbow?
Muze
# At what point are water droplets too small to make a rainbow?

(Asked by: username_0 on 2019-03-14)

This question asks [How to tell if fog is made out of water droplets or ice crystals?](https://earthscience.stackexchange.com/questions/13831/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?

**Tags:** water, light, fluid-dynamics, cloud-microphysics

> **Comments:**
> **username_1**: 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: https://www.google.com/search?biw=2400&bih=1150&tbm=isch&sa=1&ei=UJ2KXJOYG4uQ0PEPlvyS6AI&q=Sprinkler+rainbow&oq=Sprinkler+rainbow&gs_l=img.3..35i39j0i8i30l3.37218.37374..37672...0.0..0.57.110.2......1....1..gws-wiz-img.qUhOqpGA5gc  
> **username_2**: 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.  
> **username_1**: @username_0, I think you have more chances to get an answer to this in Physics SE  
> **username_3**: this is answered here https://en.wikipedia.org/wiki/Fog_bow.  
> **username_0**: @username_2 that is a start for a good answer.  
> **username_0**: @username_1 https://earthscience.stackexchange.com/questions/16308/rainbow-dynamics  

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## 1 answers

### Answer by username_2 on 2019-03-14. Score: 3 | Accepted answer

Some time ago I posted [this](https://earthscience.stackexchange.com/questions/7480/what-causes-a-rainbow-its-colours-and-its-shape/7482#7482) answer about how rainbows are formed, and the Wikipedia link username_3 username_3 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.

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1. <https://en.wikipedia.org/wiki/Light>

> **Comments:**
> **username_1**: 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?  
> **username_2**: @username_1, 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.  
> **username_4**: The smallest size of a water droplet in a cloud is about 5 um. This is much larger than the wavelength of visible light. So why don't the water droplets in clouds produce rainbows, even when the sun is in the appropriate position?  

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