II. PROPAGATION OF LIGHT TROUGH ISOTROPIC AND ANISOTROPIC MEDIA

II.1 Introduction

Definitions:

Ray path (rp): direction in which an infinite ray of light travels

Ray velocity surface (rvs): surface connecting all points reached by the light ray after a specific amount of time starting from a point source

Wave front (wf): tangent plane at point where light ray cuts through the ray velocity surface

Wave normal (wn): direction perpendicular perpendicular to the wave front

Fig. 2.1 Relationship between wave front and wave normal and between ray path and ray velocity surface

The indicatrix

The optical indicatrix illustrates how the refractive index of a transparent material/mineral varies according to the vibration direction of the light wave (assuming monochromatic light with a single wavelength).

Based on the propagation of light through various media, one can distinguish the following possibilities:

1) An optically isotropic medium

In an isotropic medium light propagates in all directions with the same velocity without polarisation (iso = equal, and tropic = to turn, rotate, or mix). This means that light starting from a single point will spread out in the shape of a ball. In an optical isotropic medium (e.g. water, glass, gas, isotropic crystals) the ray velocity surface is a sphere, where the rp and wn are identical. Since the direction of polarisation does not change in isotropic crystals, viewing between crossed polarisers (crossed nicols) will result in complete extinction independent on orientation (that is: no light is transmitted through the analyser since that will only allow radiation to pass with a vibrational direction perpendicular to that of the polariser).

2) An optically anisotropic medium

In an anisotropic medium the light ray is normally split in two two rays with different vibrational directions and different velocities (ergo refractive indices). Except for some special orientations the the rp and the wn will not coincide in an optically anisotropic medium. In this case the ray velocity surface has the shape of an ellipsoid.

Uniaxial crystals have two ray velocity surfaces; that of the ordinary ray forms a sphere, while the extra-ordinary ray forms an ellipsoid. The sphere and ellipsoid touch another at two diametrally opposite points. The line connecting these points is known as the optical axis. In the direction of the optical axis both rays have the same speed. To the uniaxial crystals belong all minerals in the hexagonal, tetragonal and trigonal crystal classes.

 Because of the symmetry operations in these systems the optical axis has to be parallel to the 6-, 4- or 3-fold rotation axis or the inversion axis. Biaxial crystals have a much more complex ray velocity surface that will be discussed later. (II.10)