Abstract: A series of matrix operations is described which enables the following optical data to be calculated for plane polarized light perpendicularly incident on a section of a transparent or opaque mineral: 1. vibration directions and refractive indices of anisotropic transparent minerals: 2. reflectivities and the state of polarization of light reflected from anisotropic opaque minerals. The data needed are the dielectric tensor, its orientation with respect to the crystal axes, the unit cell parameters and the direction of the incident light. The mathematical techniques involve the manipulation of matrices, the determination of eigenvalues and eigenvectors and, for opaque minerals, the manipulation of complex numbers. All operations can be carried out with the aid of some of the recent electronic calculators which have built-in matrix algebra procedures and complex arithmetic.