Viability and fundamental limits of critical-angle refractometry of turbid colloids

Abstract

This paper addresses a long-standing concern of whether one can measure the refractive index of a turbid colloid as if it were an equivalent homogeneous medium using standard techniques. We analyze the accuracy of determining the effective refractive index of turbid colloids when measuring the critical angle by reflection of light in an internal reflection configuration and then using Snell’s law. It is assumed that the critical angle is taken as the inflection point of the reflectance curve and that the effective refractive index of the turbid colloid is well approximated by the van de Hulst approximation. Experimental measurements are used to show the viability of measuring the inflection point of an angular-reflectance curve with highly turbid colloids. The refractive index of aqueous suspensions of and latex particles (sizes in the range of 100–500 nm) were determined with an accuracy of ±0.0025. Then, a multiple-scattering model for the coherent reflection of light from turbid colloids is used to produce 2D maps of the estimated error in determining the effective refractive index of turbid colloids by the critical angle method as a function of the size and volume-filling fraction of the colloidal particles.