Equation for the Refractive Index of Water

Abstract

The observations that β⁻¹ (∂ lnf/∂P)_T=B is a constant (of order unity, independent of temperature), and —γ⁻¹ (∂ lnf/∂T)_P=B+Cγ⁻¹, lead to an equation $${\mathrm{f(n)\equiv (n}}^2{\text{−1)/(n}}^2{\text{+2)=A}}_{\rho }^B\hspace{0.17em}\exp \mathrm{(-CT),}$$ which describes the refractive index n of water between 0° and 60°C (at any given wavelength in the visible spectrum) to within a few digits in the seventh decimal. Here ρ is the density, β=(∂ lnρ/∂P)_T and γ=—(∂ lnρ/∂T)_P. The constant C=—(d lnf/∂T)_V reflects the change in the structure of water at different temperatures. The temperature of maximum index [(∂n/∂T)_P=0] corresponds to γ=—C/B, and the minimum in the Lorenz—Lorentz specific refraction (n²−1)/(n²+2)ρ corresponds to γ=C/(1—B). The values of the parameters A, B, and C are independent of pressure up to 1100 bar in the temperature range examined. It is suggested that refractive index, or dielectric, measurements at higher pressures and temperatures may yield further information on the structure of water in terms of specific models related to the variation of B and C with the variables of state.