PLM Fundamentals:
Birefringence and Interference
What Is Birefringence? 

When light passes through anisotropic minerals it splits into TWO beams that vibrate perpendicular to each other. Because each of these beams travel in different directions in the mineral, they will encounter different resistance to their motion and so will travel at different speeds through the mineral.  
BIREFRINGENCE is the difference of the maximum and minimum indices of refraction in an anisotropic material. 

Birefringence = (RI_{max}  RI_{min}) 

What Is Retardation? 

Each of the two light beams travel at a different speed through a mineral sample. The two waves begin traveling from the base of the sample at the same time. However, the faster wave will travel farther than the slower wave in a given amount of time.  
The distance that the slow ray lags behind the fast ray by the time that the slow ray finally exits the mineral is called the RETARDATION.  
The retardation could be measured in absolute distances. This would most commonly be measured in Angstroms (10^{10}m) or nanometers (nm) (10^{9}m).  
Retardation could also be measured in relative distance compared to the light. How many wavelengths has the light wave lagged behind. Note that a wavelength is the distance over which the wave repeats itself completely. 


The greater the difference in velocity, the greater the retardation. Refractive Index is a comparative measure of the speed of light in a medium. Birefringence is a measure of the differential RI. Therefore the greater the BIREFRINGENCE of a mineral, the greater the RETARDATION.  
The further light must travel through an anisotropic grain the more the slow ray will lag behind. Thus the greater the THICKNESS of the sample, the greater the RETARDATION.  
What Is Interference? 

When the split light beams leave the mineral they recombine into a single plane polarized wave. In other words, the two waves must add together to form a single wave.  
Remember that light is a vector and so the waves must be added as vectors. If for example one segment of a light wave was vibrating upwards and a second was vibrating to the right then they would add to produce a wave that was vibrating at 45 degrees. 


The adding together of two waves to form a new single wave is called INTERFERENCE.  
In an anisotropic mineral where retardation of the slow ray occurs, the front of the fast ray emerges before the front of the slow ray. By the time the front of the slow ray emerges, the front of the fast ray has already passed. Thus when the slow ray finally emerges it cannot combine with the front of the fast ray. It must combine with whatever part of the fast ray it encounters.  
The characteristics of the light that is produced by interference will depend upon the particular orientation and magnitude of each wave when they combined. 