By making the appropriate modifications to an optical microscope, physical properties such as retardation, absorption colour, optical path boundaries, and the ability to distinguish between isotropic and anisotropic materials, can be investigated. The components necessary for polarized light microscopy include, a polarizer (positioned between the condenser and the light source), and a second polarizer, called an analyzer (positioned between the objective and the detector).
Light consists of mutually perpendicular electric and magnetic fields which propagate in all possible planes perpendicular to the direction of travel. The polarization of such a light field is said to be randomly polarized or non-polarized. When randomly polarized light passes through a polarizer, only the component parallel with the polarizing axis is transmitted. Hence, the light emerging from the polarizer is plane polarized with respect to axis of the polarizing filter. For an ideal polarizer, the transmission intensity is always 50 % that of the incident light, no matter the orientation of the polarizer.
The analyzer will either completely block or will permit the passage of some percentage of the light, depending on the angle with respect to the polarizer. The transmission intensity is maximal when θ=0° and is minimal when θ=90°, (polarizer and analyzer are crossed), thus, the ratio of transmission:incident is angle dependent (cos θ). Only the electric field component parallel with the axis of the polarizer will be transmitted through the analyzer. The transmission intensity at intermediate angles of the analyzer can be determined by using the law of Malus
Thus, by varying the angle between the transmission axis, it is possible to control the intensity of the transmitted light.
Now, consider a birefringent material, such as a calcite (CaCO3), placed into the light path. When plane polarized light impinges on the surface of the anisotropic crystal, the light ray is split into two components, called the ordinary (O-) and the extraordinary (E-) rays. The velocities of these components differ, depending on the path taken through the crystal. Because their speeds are different, they emerge from the sample out of phase with respect to the incident phase. The degree of phase change Φ depends on the thickness of the sample. If the thickness of the material is such that, a 90° (π/2) or 180° (π) phase change is introduced, the crystal is termed a quarter wave plate or half wave plate, respectively. These materials thus convert linearly polarized light into circularly polarized light and vice versa.
Because the refractive index varies with colour,
then, birefringence also varies with wavelength. The total birefringence for a particular wavelength is dependent upon the thickness of the sample and the refractive indices of the material
As the rays emerge from the sample, they are out of phase, superimposing to generate either circular or elliptically polarized light, depending on Φ. The analyzer then functions to recombine the rays, where they interfere to create an interference pattern.
When the vibration azimuths are positioned transversely, in other words, when polarizer and analyzer are crossed, the field of view is dark. However, with the introduction of a lambda plate (compensator plate), into the optical path (positioned between the objective and the analyzer) a vibrant array of colours is produced which vary depending on the orientation of the crystals, as seen in the image below. The function of the lambda plate is to introduce colour, since the human brain is not sensitive to the polarization of light.
The colourful interference field can be described by considering the following scenario;
Linearly polarized light can be resolved into two electric field components, the parallel component and the transverse component. Consider a plane-polarized light ray incident on a birefringent crystal in a direction orthogonal to that of the optical axis of the crystal. The beam will be split into two components whose electric field vectors (planes of vibration) oscillate at a right angle to one another, the parallel component and the transverse components. As the rays propagate through the crystal, the two rays become subjected to differing speeds resulting in the retardation of one ray with respect to the other, a phase difference Φ is introduced between the rays as they emerge from the sample
The ordinary ray vibrates in the plane transverse to the optical axis of the substance, whilst the extraordinary ray vibrates in the plane parallel with that of the optical axis.