# Examination of Minerals in Cross Polars

Examination of Minerals in Crossed Polars: When the analyzer is placed in the position with its plane of polarization at right angles to that of the polarizer, the polars are said to be ”crossed”. If a section of a doubly refracting mineral is placed between crossed polars, the light is doubly refracted and polarized three times as discussed below:

1. The light that enters the polarizer, is doubly refracted and polarized. The E-ray vibrates in the vibration direction of the polarizer and O-ray at right angles to it. Here O-ray is eliminated and only E-ray passes through the polarizer.
2. When this ray strikes an anisotropic mineral section, it is divided into two rays: (i) E-rays, and (ii) O-rays. They vibrate at the right angle to each other in the vibration direction of the mineral. These two rays move upward to the analyzer.
3.  At the analyzer, the third double refraction takes place and the two rays are divided into four rays: (i) E”-ray, (ii) O”-ray, (iii) E”’-ray, (iv) O”’-ray. Here the two ordinary rays are eliminated and the two extraordinary rays are rays; E”-ray and E”’-ray pass through the analyzer. Since they vibrate in the same plane (plane of analyzer) and have a fixed phase difference, they interfere. If the phase difference of the two rays is zero or integral multiple of wavelengths, darkness results, and if this phase difference is one half wavelength or any uneven multiple thereof, maximum brightness is produced.

### Case of Isotropic Minerals:

Isotropic minerals do not show double refraction. If a thin section of an isotropic mineral is viewed in crossed polars, it will appear totally dark. The reason is that the light coming from the polarizer passes through the isotropic mineral unchanged. The analyzer cuts out this light completely and darkness results. If the position of the mineral grain is changed by rotating the stage, it will remain dark through the complete rotation.

### Interference Colour:

When a thin section of an anisotropic mineral is examined in crossed polars, it generally appears bright. If the stage of the microscope is rotated, the mineral will become dark and bright four times i a complete rotation. This phenomenon can be explained with the help of this diagram;

1. Suppose the vibration direction of anisotropic crystal under examination, are at oblique angles to those of polarizer and analyser.
2. When light from the polarizer strikes the anisotropic crystal section it is broken up into two rays. These rays vibrate in mutually perpendicular planes in the vibration directions of the crystal.
3. During the passage through the crystal, the two rays have traveled with different velocities. Thus, on emerging, one ray is retarded relative to the other. These rays pass upward to the analyzer.
4. On entering the analyzer, each of these rays is broken up into two components (O-ray, and E-ray). Only those components of the two rays are transmitted, which vibrate parallel to the plane of the analyzer.
5. The two rays, which emerge from the analyzer, vibrate in the same plane. As there is a phase difference in them, they interfere with one another. The amount of phase difference depends both on the difference in velocities and on the thickness of the crystal section traversed.
6. The conditions of interference, which cause darkness vary for rays of different wavelengths. Hence when white light is used, the intensity of some wavelengths are reduced to zero, whereas the intensity of others is increased to maximum. The colours of the spectrum thus produced are called ”interference colours”.
7. There are different ”orders of interference” depending on whether the colours result from a path difference of 1λ, 2λ, 3λ, etc. These colours are called first order, second order, third order, etc colours respectively.