Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials

High-precision critical-angle refractometers, with automatic refractive index computation and readout, are now available from several manufacturers. In such instruments tight is incident from within a transparent reference medium, typically an optical prism, onto a sample material in good optical contact with the prism. The critical angle of reflection is measured at the interface between the prism of known refractive index and the sample material of unknown refractive index. Critical-angle refractometers are calibrated for transparent samples but are commonly used for measurements of refractive index in optically absorbing or optically heterogeneous materials. The instrument will then read an apparent refractive index which differs from the true refractive index of the sample. The optics of the critical-angle refractometer are investigated to quantify errors which arise from the neglect of absorption and heterogeneity in the transparent sample interpretation of the critical angle. Refractive index reading errors will be important when they become larger than the refractive index precision of modem instruments, about 10(-5). In critical-angle refractometry it is shown that this occurs for samples of surprisingly weak absorption. The critical-angle and Brewster-angle methods are compared for optically absorbing and heterogeneous samples. Errors arising from sample absorption in the Brewster-angle method are shown to be much less than in the critical-angle method.