Index of refraction - gas density formula

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Discussion Overview

The discussion revolves around the derivation of the formula relating the index of refraction to gas density, exploring both theoretical and empirical aspects of this relationship.

Discussion Character

  • Technical explanation, Exploratory, Debate/contested

Main Points Raised

  • One participant requests a derivation of the formula connecting index of refraction and gas density, referencing an external article.
  • Another participant suggests that the relationship may be empirical, pointing out the use of the word "typical" in the referenced article.
  • A different participant notes that the index of refraction is also influenced by the wavelength of light, introducing the concept of chromatic dispersion.
  • One participant provides a theoretical framework involving relative permeability and molecular polarizability, leading to a formula for the index of refraction in gases.
  • This participant further defines a variable related to the reference density of the gas, linking it to the derived formula for the index of refraction.

Areas of Agreement / Disagreement

Participants express differing views on whether the relationship is empirical or theoretical, and there is no consensus on the derivation or interpretation of the formula.

Contextual Notes

The discussion includes assumptions about the nature of gases and their properties, as well as dependencies on definitions such as molecular polarizability and reference density.

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