There are various methods of polarization; including selective absorption, double refraction, reflection, and scattering. In order to understand mineral optics, we will focus on the first two.
Selective Absorption
Some materials, certain minerals among them, have the property of strongly absorbing light vibrating in one direction and transmitting light vibrating in a perpendicular direction. This property is called pleochroism. In 1928, Edwin Land used a pleochroic material called herpathite to develop the first polarizing film. Herpathite forms long slender crystals. When these crystals are aligned parallel to each other in a thin sheet of plastic, they form a polarizing sheet in which the polarization direction is the direction along which the crystals are aligned. When light is sent through such a polarizing sheet, the electric field component parallel to the polarizing direction is transmitted and the component perpendicular to it is absorbed. Polarizing sheets consisting of elongate molecules are now used in more modern polarizing microscopes.
Image from Case Western Reserve University http://abalone.cwru.edu/
If light that is already polarized is sent through another polarizing sheet which is perpendicular to the first, no light will be transmitted.
The electric field oscillations of unpolarized light can be resolved into 2 perpendicular components. When this light is sent through a polarizing sheet, the components in one direction will be absorbed and the components in the other direction will be transmitted. The intensity of the polarized light will be half of the original intensity of the unpolarized light.
I = (1/2)Io If the light reaching a polarizing sheet is already polarized at an angle q to the polarization direction, the new intensity will be
I = Iocos2q
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