# Index of refraction - gas density formula

1. May 20, 2014

### Goodver

Could anyone please write the derivation (or forward me to the source of derivation) of the formula related these two properties.

http://www.mathpages.com/home/kmath187/kmath187.htm

thanks

2. May 20, 2014

### dauto

I think this is an empirical relation. Note the giveaway word "typical" in the first paragraph.

3. May 20, 2014

### dlgoff

4. May 20, 2014

### UltrafastPED

Let the relative permeability of the gas be ε_rel = 1 + χ, where χ is the susceptibility;
χ=α*N/V=αρ, where α is the molecular polarizability, N is the number of molecules, V the volume, and ρ=N/V is the density.

Then the index of refraction for a homogeneous, isotropic, non-magnetic dielectric such as a gas is:
n = √ε_rel = √(1 + χ)≈1 + χ/2=1+αρ/2.

Then let k = α/2ρ_0, where ρ_0 is the reference density of the gas - hence the given formula:
n ≈ 1 + k(ρ/ρ_0).