polarization ii

A narrow beam of natural light can become partially polarized when it scatters through a medium containing ultramicroscopic particles.
Degree of polarization is influenced by the angle of scattering.
Light scattered at an angle of 90° to the incident beam becomes linearly polarized.
The E vector (electric field vector) in scattered light vibrates perpendicularly to the plane defined by the propagation direction and the observation direction.
Example: Sunlight scattering in Earth's atmosphere; maximum polarization observed on clear days when the sun is near the horizon, with polarization levels between 70% and 80%.

Discovered by Biot (1815), certain mineral crystals absorb light selectively.
Example: Tourmaline crystals split natural light into two polarized components in perpendicular planes.
Crystal absorbs light polarized parallel to a specific direction while transmitting light polarized perpendicular to it.
This selective absorption is also called dichroism.
If properly thick, one component of light is completely absorbed, resulting in linearly polarized light emerging from the crystal.
Crystals exhibiting selective absorption are anisotropic.
Absorption related to electron theory: absorption is heightened when the light frequency approaches the natural frequency of the crystal's electron cloud.
The difficulty lies in growing sufficiently large dichroic crystals.

Discovered by Erasmus Bartholinus (1669) during studies on calcite crystals (Iceland spar).
Incident light on calcite splits into two refracted rays due to birefringence (double refraction).
These two rays are linearly polarized in perpendicular directions:
- O-ray: Follows Snell's law of refraction.
- E-ray: Does not follow Snell's law.
This distinction enables identification between the two rays and their polarization states.

A polarizer is an optical device that transforms unpolarized light into polarized light.
A linear polarizer produces linearly polarized light; associated with a specific direction, called the transmission axis.
When unpolarized light enters a linear polarizer, only the vibrations parallel to the transmission axis pass through; perpendicular vibrations are blocked.
An analyser identifies the direction of vibration in linearly polarized light.
Both are manufactured similarly, producing identical effects on incoming light streams.

Two main types of linear polarizers: based on birefringent or dichroic crystals.
Nicol Prism: Constructed from calcite; first designed by William Nicol (1820) through cleavage at precise angles to create a prism allowing specific polarization.
Polaroid Sheets: Made from dichroic crystals used in everyday applications like sunglasses and camera filters.
- Nicol prisms are expensive but effective in analyzing optical properties.

When unpolarized light passes through a polarizer, transmitted intensity is reduced to half the intensity of the incident light.
The polarizer blocks components of vibrations perpendicular to the transmission axis while allowing parallel components to transmit.

When polarized light passes through an analyser, intensity varies with the angle between the transmission axes of the polarizer and analyser.
Malus' law states:I = Io cos²θwhere Io is the intensity of plane polarized light and θ is the angle between the axes.
Maximum intensity occurs when axes are parallel (θ = 0°), while no light passes when they are perpendicular (θ = 90°).

An isotropic medium, like glass, refracts light as a single ray, presenting identical refractive indices in all directions, while anisotropic crystals have differing properties based on direction.
Properties involving thermal and electrical conductivity, light velocity, and refractive index exhibit directional dependence due to atomic arrangement within these crystals.
Divided into uniaxial and biaxial crystals.
- Uniaxial: one ordinary ray (o-ray) and one extraordinary ray (e-ray).
- Biaxial: both refracted rays are extraordinary rays.
Examples: Calcite and tourmaline as uniaxial crystals; mica as a biaxial crystal.

Plane intersecting the optic axis and perpendicular to crystal faces; determines interaction of light within the crystal.
Principal sections exhibit unique behavior with respect to polarization and double refraction phenomena.

Incident rays on the principal section split into o-ray and e-ray, demonstrating different paths and speeds with consequences for polarization effects.
Observing through the crystal highlights the variations in intensity (o and e images) as it rotates.

Light behaves as wave surfaces; double refracting crystals create two simultaneous wave surfaces for o-ray (spherical wave surface) and e-ray (ellipsoidal wave front).
The intersection of these surfaces defines the optic axis direction.
- Negative crystals (e-ray's refractive index < o-ray's) verses positive crystals (e-ray's refractive index > o-ray's).

Ordinary ray follows typical laws of refraction; extraordinary rays do not.
Both rays are plane polarized but in mutually perpendicular planes.
The velocities differ: o-ray's propogation speed remains constant; e-ray's varies by direction but equals o-ray's on the optic axis.

Characteristics of positive uniaxial and negative uniaxial crystals outlined, with arrows indicating velocity dynamics and refractive index distinctions, emphasizing birefringence nature.