The relation between refractive index and density of minerals related to the Earth's mantle

It is known that the density of many minerals is related to the (average) index of refraction by a linear law called the Gladstone-Dale law. It is shown that this law is generally applicable only to minerals whose anion is oxygen and whose mean molecular weight is close to 21. Another relationship, called Drude's law, which is deduced from classical dielectric theory, fits the data just as well as the empirical linear law. The correlation between density and index includes the minerals arising from various combinations of SiO2, MgO, Al2O3, Na2O, and K2O. An implication is that density controls certain physical properties of oxides, independently of composition or crystal class. This is analogous to the rule found by Birch which relates sound velocity to density and holds for the same groups of minerals.