INTRODUCTION

Anisotropic minerals are covered in Chapter 5 of Nesse.

Anisotropic minerals differ from isotropic minerals because:

1. the velocity of light varies depending on direction through the mineral;
2. they show double refraction.

When light enters an anisotropic mineral it is split into two rays of different velocity which vibrate at right angles to each other.

In anisotropic minerals there are one or two directions, through the mineral, along which light behaves as though the mineral were isotropic. This direction or these directions are referred to as the optic axis.

Hexagonal and tetragonal minerals have one optic axis and are optically UNIAXIAL.

Orthorhombic, monoclinic and triclinic minerals have two optic axes and are optically BIAXIAL.

In Lab # 3, you will examine double refraction in anisotropic minerals, using calcite rhombs.

Calcite Rhomb Displaying Double Refraction

1. Ordinary Ray, labelled omega w, n_w = 1.658
2. Extraordinary Ray, labelled epsilon e, n_e = 1.486.

Vibration Directions of the Two Rays

The vibration directions for the ordinary and extraordinary rays, the two rays which exit the calcite rhomb, can be determined using a piece of polarized film. The polarized film has a single vibration direction and as such only allows light, which has the same vibration direction as the filter, to pass through the filter to be detected by your eye.

1. Preferred Vibration Direction NS

   With the polaroid filter in this orientation only one row of dots is visible within the area of the calcite rhomb covered by the filter. This row of dots corresponds to the light ray which has a vibration direction parallel to the filter's preferred or permitted vibration direction and as such it passes through the filter. The other light ray represented by the other row of dots, clearly visible on the left, in the calcite rhomb is completely absorbed by the filter.

   
   
2. Preferred Vibration Direction EW

   With the polaroid filter in this orientation again only one row of dots is visible, within the area of the calcite coverd by the filter. This is the other row of dots thatn that observed in the previous image. The light corresponding to this row has a vibration direction parallel to the filter's preferred vibration direction.

It is possible to measure the index of refraction for the two rays using the immersion oils, and one index will be higher than the other.

1. The ray with the lower index is called the fast ray
   • recall that n = V_vac/V_medium
     If n_{Fast Ray} = 1.486, then V_{Fast Ray} = 2.02X10¹⁰ m/sec
2. The ray with the higher index is the slow ray
   • If n_{Slow Ray} = 1.658, then V_{Slow Ray} = 1.8 1x10¹⁰ m/sec

Remember the difference between:

• vibration direction - side to side oscillation of the electric vector of the plane light
  and
• propagation direction - the direction light is travelling.

Electromagnetic theory can be used to explain why light velocity varies with the direction it travels through an anisotropic mineral.

1. Strength of chemical bonds and atom density are different in different directions for anisotropic minerals.
2. A light ray will "see" a different electronic arrangement depending on the direction it takes through the mineral.
3. The electron clouds around each atom vibrate with different resonant frequencies in different directions.

Velocity of light travelling though an anisotropic mineral is dependant on the interaction between the vibration direction of the electric vector of the light and the resonant frequency of the electron clouds. Resulting in the variation in velocity with direction.

Can also use electromagnetic theory to explain why light entering an anisotropic mineral is split into two rays (fast and slow rays) which vibrate at right angles to each other.