# How does wind speed affect the velocity of light?

As you know, there is a maximum speed things can go called $c$, the "speed of light." Light in a vacuum goes $c$. Light in the atmosphere, however, goes a little less than $c$.

My question is: what effect does wind have on light's velocity? Simply adding the wind's velocity to light's would not even be remotely close, since a 10 mph tail wind would probably push it over $c$.

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If the air is not moving, we know the light moves at a speed $v=c/n$, where $n$ in the index of refraction of the air. Now if the air is moving at a speed $u$ relative to you, and the light is propagating in the same direction, then you can find the apparent speed of light by the relative addition of velocities formula. In this case, you will find the apparent speed of light to be $$\frac{v+u}{1+\dfrac{uv}{c^2}}.$$

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Wouldn't turbulence and preassure be relevant for the refractive index? –  jinawee May 2 '14 at 20:25
That's a good point. In reality wind is not just a uniform motion of air at a constant speed. The pressure and temperature will be non-uniform, and this will cause the index of refraction to be non-uniform. This effect on the speed of light is probably greater than the effect I talked aobut in my answer. However, it is not as easy to get a clean answer as to what the speed of light should be with these effects taken into account. –  NowIGetToLearnWhatAHeadIs May 2 '14 at 20:52
Is there a reason why velocity addition applies to light in a moving medium? –  Brian Funt May 30 '14 at 18:26
@BrianFunt I think I should have explained this better. Basically imagine you are standing on train tracks with the wind blowing at some speed $u$. Now you are wondering what the speed of light is. Luckily your friend is coming by on a train moving at the same speed $u$. You ask him what the speed of light is, and since he sees no wind the answer is easy: $v=c/n$. Now we have the light moving at a speed $v$ in a frame which is moving at a speed $u$ with respect to $u$, and we want to know what is the velocity in your frame. The asnwer is given by the relativistic velocity addition formula. –  NowIGetToLearnWhatAHeadIs May 30 '14 at 20:58
Is it just coincidental that the group velocity of light is being treated similarly to an 'object' moving at speed $v$? –  Brian Funt May 30 '14 at 21:16

Two things:

1. Medium motion does 'drag' speed of light. http://en.wikipedia.org/wiki/Light-dragging_effects
2. Speeds of medium and c are not linearly added. Use Lorentz Transformation: http://en.wikipedia.org/wiki/Lorentz_transformation
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If you could expand this answer to more than just two links, that would be helpful. Can you post the relevant info from those links here? –  iamnotmaynard May 2 '14 at 21:58

the only way to find out is with an experiment, and no such interferometer exists. although how about recording he speed of light, then putting a hight speed gush through the lad - like a hurricane? And then see.

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Or you could just do math. –  PyRulez May 26 '14 at 15:17

## protected by Qmechanic♦May 25 '14 at 14:54

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