Model Answer
0 min readIntroduction
Birefringence, also known as double refraction, is an optical property of anisotropic materials where light is split into two rays, each traveling at a different velocity. This phenomenon arises due to variations in refractive index depending on the direction of light propagation within the crystal. In petrology, understanding birefringence is fundamental to mineral identification and analysis using a petrological microscope. The indicatrix, a geometrical representation of refractive indices, provides a powerful tool to visualize and interpret the birefringence exhibited by minerals, particularly uniaxial minerals, and how it changes with the orientation of the thin section relative to the polarized light.
Understanding Birefringence in Uniaxial Minerals
Uniaxial minerals possess a single optic axis, around which the refractive index is constant. This contrasts with biaxial minerals which have two optic axes. The difference between the maximum and minimum refractive indices in a uniaxial mineral is termed birefringence (Δ = no - ne, where no is the ordinary refractive index and ne is the extraordinary refractive index). The magnitude of birefringence dictates the intensity of interference colors observed under crossed polars.
The Indicatrix: A Visual Representation
The indicatrix is a three-dimensional geometrical figure that represents the refractive indices of a mineral in all directions. For a uniaxial mineral, the indicatrix is an ellipsoid of revolution with the optic axis as its axis of symmetry.
- Ordinary Ray: The ordinary ray (o-ray) experiences a constant refractive index (no) regardless of its direction. On the indicatrix, this is represented by a sphere inscribed within the ellipsoid.
- Extraordinary Ray: The extraordinary ray (e-ray) experiences a variable refractive index (ne) depending on its direction. This is represented by the ellipsoid itself.
Crystallographic Orientation and Birefringence
The birefringence observed in a thin section is highly dependent on the crystallographic orientation of the mineral grain. The orientation of the optic axis relative to the vibration directions of the polarized light significantly influences the interference colors.
1. Optic Axis Parallel to the Extinction Direction
When the optic axis is parallel to the extinction direction (the direction of maximum absorption of light), the interference colors are at their minimum. This occurs because the slow and fast rays are separated by the smallest angle. The mineral appears dark under crossed polars.
2. Optic Axis Inclined to the Extinction Direction
As the optic axis is inclined to the extinction direction, the angle between the slow and fast rays increases, leading to higher-order interference colors. The observed color depends on the thickness of the thin section (t) and the birefringence (Δ) according to the following formula:
Retardance (R) = t * Δ
Color = R / λ (where λ is the wavelength of light)
3. Indicatrix Diagram and Orientation
The indicatrix diagram helps visualize these effects. Imagine a plane representing the thin section cutting through the indicatrix. The shape of the intersection determines the observed birefringence.
(Note: This is a placeholder image link. A hand-drawn, labelled diagram would be ideal for a UPSC answer.)
By rotating the thin section on the microscope stage, the orientation of the indicatrix changes, resulting in a cyclic change in interference colors. This is the basis for identifying minerals and determining their optical properties.
Impact of Mineral Composition on Birefringence
The chemical composition of a uniaxial mineral directly influences its birefringence. For example, calcite (CaCO3) exhibits a higher birefringence than aragonite (CaCO3) due to differences in their crystal structures and bonding. Similarly, the presence of impurities or solid solutions can alter the refractive indices and, consequently, the birefringence.
Conclusion
In conclusion, the birefringence of a uniaxial mineral is a crucial optical property used in petrological analysis. The indicatrix diagram provides a powerful tool for understanding how the refractive indices vary with crystallographic direction. The observed interference colors are directly related to the mineral’s birefringence and its orientation within the thin section. Accurate interpretation of these optical properties allows for precise mineral identification and provides valuable insights into the geological history of rocks.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.