OPTICAL MINERALOGY

LECTURE 9

RETARDATION

Anisotropic Mineral Properties:

1) Hexagonal, and tetragonal have one optic axis

Examples: quartz, beryl, apatite, corundum and calcite

2)  velocity of light varies dependent on direction through mineral

3) they show double refraction

The two rays must therefore be plane polarized and vibrate at 90 degrees to each other(see figure below) .   The ray vibrating in the lower index direction is called the fast ray (light blue colored) and the ray travelling in the higher index is called the slow ray (brick colored)

while in the media of thickness "d" the fast ray oscillates one lambda and the slow ray two lambda.  Therefore, the fast ray exits the media first and a full one lambda of the wave form is back in the air media before the slow ray arrives at the top surface.  that difference is referred to as the retardation or the "delta"(D) (shown above).

From this relationship the author of your text derives the relationships which exist between the retardation (D), thickness of the sample (d),  refractive index of the slow ray (ns), and refractive index of the fast ray (n f)

D = d(ns - n f)

The  term (ns - n f) is called birefringence and is the difference between the indices of the slow and fast rays.  

Interference Phenomena:

The color seen in anisotropic minerals when viewed between crossed nicols.  The colors seen are called interference colors and are the result of light being split into two rays which travel at differing velocities through the mineral.

To better understand this, lets begin with monochromatic light.

In the above figure we will send e-w plane polarized light through a uniaxial mineral with preferred vibration directions; fast ray oriented ne-sw (green arrow in lower block) and a slow ray oriented nw-se (gold arrow in lower block).  for clarity in seeing the wave forms the next two blocks up represent an exploded view a single block  in order to better see the two vibration directions.  NW-SE blue-green plane shows the wave form for the slow direction and the light-gold plane contains the wave form of the fast ray. the retardation is one lambda.  The light emerging from the top of the mineral recombines and vibrates EW. if  we tried to view this light under crossed nicols the field of view would be dark because the NS analyzer would block the EW vibrating wave.

Same principle as previous diagram, but this time the D is l/2. Note the left block in the middle row contains 1.5l's and the right block 1 l .  The resulting recombination at the top of the mineral produces a N-S vibrating ray.  When viewed under crossed nicols we would see the brightest intensity of the monochromatic light. 

cross section of a quartz wedge

D = d(ns - n f) = i l   when i is an integer the slow ray is retarded exactly one l for monochromatic light the emergent light from the top of the grain vibrates e-w and no light will pass through the n-s oriented upper-polarizer. If  D = (i+½)l then the emergent light vibrates parallel to upper polarizer and maximum brightness occurs..

Between these extremes the light is either elliptically or circularly polarized and intermediate amounts of light are transmitted under crossed nicols.

Given: retardation D is proportional the thickness d and l. We use polychromatic light and therefore all the other lambdas are present and for mineral of a constant thickness "d"     wavelengths will be retarded differing amounts meaning some are in phase and others out of phase.

% transmission by the upper polarizer of the different waelengths in a beam of white light that was passed through a crystal of retardation 550 nm.

The resultant blend of colors is shown in the small rectangle in center of diagram.  the same color which results when the 1l accessory plate is inserted.