# Snell's law

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?

## Answers and Replies

Redbelly98
Staff Emeritus
Homework Helper
A Google search on
air "refractive index"
led me here:
http://www.strw.leidenuniv.nl/~mathar/progs/prWaterWeb.html [Broken]
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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olgranpappy
Homework Helper
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

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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
Staff Emeritus
Homework Helper
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?

olgranpappy
Homework Helper
i gave it to you

Redbelly98
Staff Emeritus