Empirical Model for Total Internal Reflection (TIR) from Highly Turbid Media

Recently we introduced a new empirical model for total internal reflection (TIR) from a highly turbid medium [W. Calhoun, et al, \emph{Opt. Lett.} {\bf 35}, 1224-1226 (2010); \emph{ibid} {\bf 36}, 3172 (2011)]. The key feature of our model is that it incorporates into Fresnel theory the effect of angle-dependent penetration of the incident light into the medium. Here we show that the TIR data is, for the first time, well described by a model which has no extraneous fitting parameters. As a further check we use our model to extract the particle size for a highly turbid aqueous solution of monodisperse polystyrene microspheres of known size. Next we apply our model to a first in-situ measurement of average particle size in a widely used intravenous human nutrient