Determination of the adiabatic piezo-optic coefficient of liquids

The variations in the refractive index of a liquid under external force may be expressed either in terms of the applied pressure or of the resulting change of density, in other words as proportional to the piezo-optic coefficient (∂μ/∂p) or to the elasto-optic coefficient ρ(∂μ/∂ρ). The ratio of the two coefficients is the compressibility β of the liquid; according as the pressure is applied adiabatically or isothermally, we have (∂μ/∂p)ϕ = ρ(∂μ/∂ρ)ϕ. βϕ (Entropy ϕ Constant) (∂μ /∂p)t = ρ(∂μ/∂ρ)t. βt (Temperature t Constant). In some important optical problems, e.g. the diffraction of light by ultra­sonic waves, or the diffusion of light resulting from the Debye waves in a liquid, we are concerned with compressions and rarefactions occurring under adiabatic conditions and with the resulting changes of refractive index. As a rough approximation, the two elasto-optic coefficients may be taken to be equal and the two piezo-optic coefficients to be therefore in the ratio of the adiabatic and isothermal compressibilities. More exactly, however, these relations would not subsist, as a consequence of the refractive index of a dense fluid being in general a function of both density and temperature, and not of the density alone.