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The optical density of a medium is quantified by its refractive index $n$. Does it have any correlation with the mass/number density of the medium? In other words is an optically denser medium must have a greater mass density compared to an optically rarer medium?

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Index of refraction is $ n = \sqrt{\varepsilon}\sqrt{\mu}$, where $\varepsilon$ and $\mu$ are relative permittivity(dielectric constant) and permeability. Usually materials have $\mu = 1$. Now the question is, is the dielectric constant dependent on mass density? Not directly. It depends on number density and atomic (molecular) polarizability. The polarizability does depend on mass. In simple models, it is inversely proportional to mass (search lorentz oscillator model).

Optical density also depends on the incident light frequency. If the incident light frequency is close to the resonance of the medium, the polarizability becomes large and so does the index of refraction. Lithium atoms will appear dense to laser with 671 nm wavelength. But not rubidium (its main resonances are 780 nm and 795 nm. There are other ones, but those two (D-line resonances) have most of the oscillator strengths) [note: lithium is roughly 12 times lighter than rubidium].

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  • $\begingroup$ I fixed some typos in your answer. Hope you don't mind. $\endgroup$ – mithusengupta123 Jul 29 '18 at 14:36

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