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Index of refraction - gas density formula

  1. May 20, 2014 #1
    Could anyone please write the derivation (or forward me to the source of derivation) of the formula related these two properties.


    the first fomula in this article.

  2. jcsd
  3. May 20, 2014 #2
    I think this is an empirical relation. Note the giveaway word "typical" in the first paragraph.
  4. May 20, 2014 #3


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  5. May 20, 2014 #4


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    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).
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