Isosbestic-like point in the polarized reflectance spectra of monoclinic crystals--A quantitative approach

If two overlapping bands originate from transition moments that are perpendicular and lie along the principal axes of the infinity frequency dielectric tensor, an isosbestic-like point (ILP) appears in the overlaid polarized IR reflectance spectra of single crystals. These conditions can also be met in principle in case of the reflectance from the ac-plane of a monoclinic crystal despite of the crystal's low symmetry. In order to determine the transition moment directions, diagonalization of the infinity frequency dielectric tensor should be performed. It is shown that a critical magnitude for the appearance of ILP is the angle of incidence. An increase of this angle leads to a transformation of the ILP to an isosbestic-like region, which eventually vanishes at higher incidence angles. Polarized reflectance spectra of gypsum (CaSO4.2H2O), recorded from the ac crystal face, were used to verify the theoretical results.