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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.

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

    the first fomula in this article.

    thanks
     
  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

    dlgoff

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  5. May 20, 2014 #4

    UltrafastPED

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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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