Effect of the gradient of complex refractive index at boundary of turbid media on total internal reflection

We analyze the existence of non-uniformity at the boundary of turbid media, and develop a gradient complex refractive index multilayered model in terms of this fact. Our model reveals the physics mechanism of the discrepancies between experimental data above the critical angle and the fitting curve with Fresnel's Formula. Also, from the perspective of the energy flow, reflectance R is obtained by the simplified models. We get complex refractive indexes and reflectance curves by fitting experimental data of 20% and 30% Intralipid solutions and rutile TiO₂ powder suspension with two different methods. Compared with Fresnel's Formula, our model can fit experimental data better.