How to find the index of refraction of air from pressure and temperature

[Az83]

For Snell's law n2sin(theta2)=n1sin(theta1), I know that air has an index of refraction of approximately 1. But how do I find the actual value for the index of refraction if I know the temperature jump and pressure? I know that from what I am given, I can find the densities of the air, but then how do I use the densities to find the index of refraction?

 

[Redbelly98]

A Google search on
air "refractive index"
led me here:
http://www.strw.leidenuniv.nl/~mathar/progs/prWaterWeb.html
Calculates (n-1) depending on temperature, pressure, humidity, and even CO2 content of the atmosphere!

Do you happen to have a particular application or use in mind? Eg., ray tracing calculation, atmospheric distortion, solving a homework problem, other?

 

[olgranpappy]

well. I think you could look up the dielectric constant ($\epsilon$, where $n^2=\epsilon$) at different densities. but also, if you know the dielectric constant at some given number density ($n_1$) then to find it at a different density you could use
$$\frac{\epsilon(n_2)-\epsilon(n_2)}{\epsilon(n_1)-1}=\frac{n_2-n_1}{n_1}$$

...and, sorry for using the symbol n for two different things... my bad, in the equation it is number density, not index of refraction

 

[Az83]

this question is for a homework problem. It seems that every source I look at, the dielectric constant for air at 1 atm is 1.00059. Is this value safe to assume for all temperatures?

 

[Redbelly98]

this question is for a homework problem. It seems that every source I look at, the dielectric constant for air at 1 atm is 1.00059. Is this value safe to assume for all temperatures?

No, it will change with temperature and pressure. The denser the air, the higher the value.

 

[Az83]

Is there an equation that relates the density to the index of refraction?

 

[olgranpappy]

i gave it to you

 

[Redbelly98]

Is there an equation that relates the density to the index of refraction?

You can do pretty well by assuming (n-1) is proportional to the air density.