nepsilon refers to the maximum or minimum index of refraction for the extraordinary ray, the value recorded in the mineral descriptions in the text.
nepsilon' refers to an index of refraction for the extraordinary ray which is between nomega and nepsilon.
For uniaxial minerals any orientation will provide nw, but only one orientation, cut parallel to the c-axis will yield nepsilon maximum. This orientation is the one which exhibits the highest interference colour as delta (birefringence), is greatest, and therefore DELTA (retardation) is greatest
Hexagonal and tetragonal systems are characterized by a high degree of symmetry about the c-axis. Within the 001 or 0001 plane, at 90° to the c-axis, uniform chemical bonding in all directions is encountered.
Light Paths Through a Mineral
Light travelling along the c-axis is able to vibrate freely in any direction within the 001 or 0001 plane.
No preferred vibration direction allows light to pass through the mineral as if it were isotropic, this orientation has the lowest interference colour - black to dark grey.
If the light passes at some angle to the c-axis, it encounters a different electronic configuration and is split into two rays of different velocities.
The vibration vector of the ordinary ray is parallel to the 001 or 0001 plane, i.e. perpendicular to the c-axis. The extraordinary ray vibrates across these planes, parallel to the c-axis.
The ordinary ray has the same velocity regardless of the path it takes, because it always vibrates in the same electronic environment.
The extraordinary ray velocity varies depending on the direction. If the light travels nearly parallel to the c-axis, the extraordinary ray vibrates ~ parallel to 001 or 0001, so that nepsilon'~nomega.
If the light travels at right angles to the c-axis, the extraordinary ray vibrates across the 001 or 0001 plane and nepsilon is most different from nomega.
For intermediate angles to the c-axis:
Whether the extraordinary ray has a higher or lower RI than the ordiniary ray depends on the chemical bonding and the crystal structure.
In the lab you will determine the indices of refraction for a uniaxial mineral using grain mounts and the immersion method.