On the analytical study of the uniaxial indicatrix

Abstract

This paper deals with theoretical considerations on the application of analytical method to uniaxial crystals. All the complicated calculation involved with biaxial crystals is reduced to a second degree equation. Each of its roots represents a possible position of the optical axis. Analytical determination is made, too, for the selection of one of the roots. The determination of total birefringence is studied. Its expression takes very simple analytical forms. It was concluded, finally, that the optical sign of the mineral is the same as the sign of its partial birefringence at the position φ = θ = ψ = 0.