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Is there any relation between Refractive index and density of a material? It is not found to be proportional in my experimental results. Is there any equation to relate these parameters?

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I'm not sure about solids and liquids as they are almost incompressible, but for gases, it should be varying with pressure and temperature. Since gas density is also a function of pressure and temperature, I expect it to be a factor (See this article for example). I hope someone familiar can explain further.

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Sure, for low enough densitites the relationship is roughly linear a fact that is sometimes used in gas Cerenkov detectors for tuning the threshold. – dmckee Dec 27 '12 at 18:20

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