text: In the Gladstone–Dale relation, , the index of refraction (n) or the density (ρ in g/cm) of miscible liquids that are mixed in mass fraction (m) can be calculated from characteristic optical constants (the molar refractivity k in cm/g) of pure molecular end-members. For example, for any mass (m) of ethanol added to a mass of water, the alcohol content is determined by measuring density or index of refraction (Brix refractometer). Mass (m) per unit volume (V) is the density m/V. Mass is conserved on mixing, but the volume of 1 cm of ethanol mixed with 1 cm of water is reduced to less than 2 cm due to the formation of ethanol-water bonds. The plot of volume or density versus molecular fraction of ethanol in water is a quadratic curve. However, the plot of index of refraction versus molecular fraction of ethanol in water is linear, and the weight fraction equals the fractional density
  In the 1900s, the Gladstone–Dale relation was applied to glass, synthetic crystals and minerals. Average values for the refractivity of oxides such as MgO or SiO give good to excellent agreement between the calculated and measured average indices of refraction of minerals. However, specific values of refractivity are required to deal with different structure-types, and the relation required modification to deal with structural polymorphs and the birefringence of anisotropic crystal structures.
  In recent optical crystallography, Gladstone–Dale constants for the refractivity of ions were related to the inter-ionic distances and angles of the crystal structure. The ionic refractivity depends on 1/d, where d is the inter-ionic distance, indicating that a particle-like photon refracts locally due to the electrostatic Coulomb force between ions.