Finding the Index of Refraction from Pressure & Temp

AI Thread Summary
To find the index of refraction of air based on temperature and pressure, one can start with Snell's law and the known dielectric constant of air, which is approximately 1.00059 at 1 atm. The index of refraction can be derived from air density, as it is proportional to the density changes due to temperature and pressure variations. A suggested method involves using the relationship between the dielectric constant and number density to calculate the refractive index at different conditions. It is important to note that the dielectric constant will vary with temperature and pressure, so the assumption of a constant value is not valid across all conditions. Understanding these relationships is crucial for applications such as ray tracing and atmospheric distortion analysis.
Az83
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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?
 
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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?
 
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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
<br /> \frac{\epsilon(n_2)-\epsilon(n_2)}{\epsilon(n_1)-1}=\frac{n_2-n_1}{n_1}<br />

...and, sorry for using the symbol n for two different things... my bad, in the equation it is number density, not index of refraction
 
Last edited:
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?
 
Az83 said:
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.
 
Is there an equation that relates the density to the index of refraction?
 
i gave it to you
 
Az83 said:
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.
 

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