Unit 4 Polarization of Light | Physical Optics 1st Sem | Bachelor of Optometry

Polarization of Light

✦ Introduction

Polarization is a unique property of light that describes the orientation of its oscillations. While sound waves are longitudinal (oscillate in the direction of propagation), light is a transverse wave, meaning it vibrates perpendicular to its direction of travel. These vibrations occur in all directions perpendicular to the light’s path in natural (unpolarized) light. When this random vibration is restricted to a single plane or in a predictable pattern, the light is said to be polarized.

✦ What Is Unpolarized vs Polarized Light?

• Unpolarized Light: Light emitted by natural sources such as the sun, lamps, or fire has electric field vectors vibrating in multiple planes.
• Polarized Light: If the vibration of light waves is confined to a single plane, the light is said to be plane-polarized or linearly polarized.

✦ Methods of Polarization

1. Polarization by Reflection: When unpolarized light strikes a smooth, transparent surface like glass or water at a particular angle called Brewster’s Angle, the reflected light becomes polarized. This principle is used in polarizing sunglasses to block glare.
2. Polarization by Refraction: When light enters a new medium (e.g., air to glass), it gets partially polarized due to refractive differences.
3. Polarization by Scattering: Sunlight scattered by air molecules gets polarized, explaining why the sky appears blue and polarized at 90° from the sun.
4. Polarization by Transmission: Polarizing filters (e.g., Polaroid sheets) allow only aligned components of light through. These are used in 3D glasses, photography, and LCD displays.
5. Polarization by Double Refraction (Birefringence): Some crystals like calcite split light into two rays—ordinary and extraordinary—due to differing refractive indices.

✦ Types of Polarized Light

• Plane (Linear) Polarized Light: Oscillations occur in only one plane.
• Circularly Polarized Light: Electric field rotates in a circle as the wave propagates.
• Elliptically Polarized Light: Electric field traces an ellipse—combining features of linear and circular polarization.

✦ Practical Importance in Optometry and Optics

• Sunglasses and Optical Filters: Polarized lenses reduce glare and enhance visual comfort.
• Microscopy: Polarized light microscopes help study birefringent materials like fibers or crystals.
• LCD Displays: Liquid crystals use polarization to control image formation.
• Stress Analysis: Polarized light reveals internal stress patterns in transparent plastics or glass.
• 3D Cinema Glasses: Use circular polarization to project different images to each eye for a 3D effect.

✦ Summary

Polarization is a fundamental phenomenon in the study of light, helping us understand its wave nature and interactions with various media. It has wide-ranging applications in vision science, photography, instrumentation, and display technologies. The study of how light is polarized deepens our understanding of optical materials and enhances diagnostic tools in optometry.

Double Refraction (Birefringence)

✦ Concept Overview

Double refraction, or birefringence, is a phenomenon where a single ray of unpolarized light entering certain crystals splits into two rays, each traveling in different directions and at different speeds. First observed in calcite, it provides key evidence of light's wave nature.

✦ What Happens in Double Refraction?

When unpolarized light enters a birefringent material:

• Ordinary Ray (O-ray): Follows Snell’s law and travels uniformly.
• Extraordinary Ray (E-ray): Deviates due to crystal orientation and varies in speed.

Both rays are plane polarized in perpendicular directions.

✦ Birefringent Crystals

• Calcite (CaCO₃)
• Quartz (SiO₂)
• Tourmaline

✦ Principal Axis / Optic Axis

The optic axis is the direction in a birefringent crystal along which no splitting occurs and light behaves as in an isotropic medium.

✦ Nicol Prism

A Nicol Prism is made of calcite and uses Canada Balsam to block the O-ray via total internal reflection. It allows only the E-ray to pass, generating plane polarized light. It’s used in polarimeters and early optical instruments.

✦ Mathematical Concept

If:
μ_o = refractive index of ordinary ray,
μ_e = refractive index of extraordinary ray,
Then birefringence is:

Δμ = μe - μo

✦ Applications of Double Refraction

• Photoelasticity: Analyzing internal stress in plastics or lenses.
• Polarizers: Creating optical filters (e.g., Nicol prism, wave plates).
• Optical Mineralogy: Identifying minerals under polarized microscopes.
• LCD Screens: Use of birefringence to control light in displays.
• Ophthalmology: Analyzing corneal birefringence for eye health assessments.

✦ Summary

Double refraction reveals the anisotropic nature of certain crystals and the behavior of light in such media. Its applications in diagnostics, displays, and optical instruments make it a key concept in optometry.

Brewster’s Law

✦ Introduction

Brewster’s Law describes how light becomes fully plane-polarized when it reflects off a surface at a specific angle. This concept is essential in understanding polarization by reflection and is widely applied in photography, sunglasses, and optical instruments.

✦ Statement of Brewster’s Law

When unpolarized light is incident on a transparent surface at a specific angle (called the Brewster angle), the reflected light becomes completely plane-polarized, and the reflected and refracted rays are at right angles to each other.

✦ Brewster’s Angle (Polarizing Angle)

The angle at which this full polarization occurs is called the Brewster angle. At this angle:

• The reflected light is completely polarized.
• The reflected and refracted rays are at 90° to each other.

✦ Mathematical Expression

Let:
θ_B = Brewster angle
n₁ = refractive index of the incident medium
n₂ = refractive index of the second medium

&tan(θB) = n2 / n1

If the incident medium is air:

θB = tan-1(n2)

Example: For glass (n = 1.5), Brewster angle ≈ 56.3°

✦ Experimental Observation

• Reflected light at Brewster’s angle is completely plane-polarized.
• The refracted light is partially polarized.
• Using an analyzer, the polarized nature of the reflected beam can be verified by its intensity variation upon rotation.

✦ Applications of Brewster’s Law

• Polarizing Sunglasses: Reduce glare from roads, water, or glass.
• Photography: Polarizing filters minimize reflections and enhance image contrast.
• Optical Coatings: Anti-reflection coatings are optimized at Brewster's angle.
• Laser Optics: Brewster windows transmit polarized light with minimal reflection.
• Telescopes & Microscopes: Reduce stray reflections and enhance image clarity.

✦ Summary

Brewster’s Law explains how light becomes polarized by reflection, making it a powerful concept in both theoretical and applied optics. Its use in polarizing lenses, photography, and laser systems is crucial in vision science and instrumentation.

Nicol Prism

✦ Introduction

A Nicol Prism is an optical device used to produce plane-polarized light by eliminating the ordinary ray through total internal reflection. Invented by William Nicol in 1828, it was widely used before the advent of Polaroid sheets.

✦ Construction of a Nicol Prism

• Made from a calcite crystal (a birefringent material).
• Cut diagonally and rejoined using Canada Balsam.
• Canada Balsam has a refractive index (~1.55) between the refractive indices of the ordinary and extraordinary rays in calcite.

✦ Working Principle

1. Unpolarized light enters the prism and splits into ordinary ray (O-ray) and extraordinary ray (E-ray).
2. The O-ray hits the Canada Balsam layer and undergoes total internal reflection.
3. The E-ray passes through the prism and emerges as plane-polarized light.

✦ Uses of Nicol Prism

• Polarizer: Produces plane-polarized light from unpolarized sources.
• Analyzer: Determines the orientation of polarization when paired with another Nicol prism.
• Polarimeters: Measures optical rotation in substances like sugar solutions.
• Scientific Experiments: Birefringence, optical activity, and polarization interference studies.
• Microscopes & Telescopes: Used in early optical devices for clear polarized imaging.

✦ Limitations

• Fragile and expensive to manufacture.
• Cannot handle wide beams or high-intensity light sources.
• Wavelength-sensitive due to the nature of calcite and Canada Balsam.
• Replaced in modern use by Polaroid filters and liquid crystal technologies.

✦ Summary

The Nicol prism is a classic device in polarization optics. It uses principles of double refraction and internal reflection to isolate a single plane of polarized light. Though obsolete in most modern tools, it remains an essential concept in the foundation of optical physics.

Polarizer and Analyzer

✦ Introduction

Polarizers and Analyzers are essential optical components used to control and examine the polarization of light. While a polarizer creates polarized light, an analyzer detects or measures its polarization.

✦ What is a Polarizer?

A Polarizer converts unpolarized light into plane-polarized light.

Types of Polarizers:

• Nicol Prism: Uses birefringence and internal reflection to eliminate one ray.
• Polaroid Sheet: Embedded with aligned molecules that absorb one direction of light.
• Tourmaline Crystal: Naturally polarizes light by absorbing one component.

The polarizer filters out all vibrations except those aligned with its transmission axis, producing linearly polarized light.

✦ What is an Analyzer?

An Analyzer is a second polarizer used to verify and analyze the polarization of light.

• When the analyzer’s axis is parallel to the light’s plane, maximum light is transmitted.
• When it’s perpendicular, light is blocked.

✦ Malus's Law

The transmitted intensity of light through an analyzer is given by:

I = I0 cos²(θ)

Where:

• I = Transmitted intensity
• I₀ = Incident light intensity
• θ = Angle between polarizer and analyzer axes

✦ Combined Use: Polarizer–Analyzer System

This system is used in many optical instruments and experiments:

• Polarizer: Produces polarized light.
• Sample: The medium under test (e.g., optical material, biological tissue).
• Analyzer: Measures the effect on the light after passing through the sample.

✦ Applications

• Photoelasticity: Study of stress patterns in transparent materials.
• Ophthalmic Diagnosis: Corneal and lens birefringence analysis.
• LCD Technology: Image formation using polarizer sheets.
• Polarimeters: Measure optical rotation in chiral substances.
• Microscopy: Polarizing microscopes for crystals and tissues.

✦ Summary

Polarizers and analyzers are critical components in the manipulation and detection of polarized light. They serve as the backbone for optical experiments and applications in science and healthcare.

Huygens’ Explanation of Double Refraction

✦ Introduction

Double refraction is the phenomenon where light splits into two rays in anisotropic materials. Christiaan Huygens explained this behavior using his wave theory of light, introducing the concept of different wavefronts within crystals.

✦ Huygens’ Principle (Recap)

Every point on a wavefront acts as a source of secondary wavelets. The new wavefront is the tangent surface to these secondary waves.

Huygens extended this to anisotropic media to explain how double refraction occurs in crystals like calcite.

✦ Behavior in Isotropic vs Anisotropic Media

• Isotropic Media: Same speed in all directions. Wavefront = spherical.
• Anisotropic Media: Speed depends on direction. Wavefronts = spherical (O-ray) and ellipsoidal (E-ray).

✦ Ordinary and Extraordinary Rays

• Ordinary Ray (O-ray): Spherical wavefront, obeys Snell’s Law, constant velocity.
• Extraordinary Ray (E-ray): Ellipsoidal wavefront, does not obey Snell’s Law, velocity varies with direction.

✦ Role of Optic Axis

In uniaxial crystals like calcite, the optic axis is the direction along which the refractive indices for both rays are equal. Light traveling along this axis does not split.

✦ Applications

• Understanding birefringence behavior in crystals.
• Designing Nicol prisms and polarizing devices.
• Explaining interference in polarizing microscopes.
• Evaluating optical properties in optometry and mineralogy.

✦ Summary

Huygens' explanation of double refraction was a foundational concept in wave optics. It introduced the idea that different wavefront shapes explain why light splits into two rays with different velocities and polarizations. This theory still underpins modern optical instruments and education.

Elliptically and Circularly Polarized Light

✦ Introduction

When light waves have electric field components in two perpendicular directions with a phase difference, the result is either elliptically or circularly polarized light. These types go beyond basic linear polarization and are essential in modern optics.

✦ Basic Concept

Two perpendicular linear vibrations (X and Y directions) combine to form different polarization states depending on their amplitude and phase difference.

✦ Circularly Polarized Light

• Equal amplitude components
• Phase difference = 90° (π/2 radians)
• The electric field vector traces a circle
• May be right-handed or left-handed depending on phase relationship

✦ Elliptically Polarized Light

• Unequal amplitudes
• Phase difference ≠ 0° or 180°
• The electric field vector traces an ellipse
• Most general form of polarized light

✦ Comparison Table

Polarization Type	Amplitude	Phase Difference	Shape
Linear	Any	0° or 180°	Straight Line
Circular	Equal	90°	Circle
Elliptical	Unequal	≠ 0°, ≠ 180°	Ellipse

✦ Generation

• Quarter-Wave Plate: Converts linear to circular (if input is at 45°)
• Half-Wave Plate: Creates elliptical polarization by altering phase

✦ Applications

• 3D Cinemas: Circularly polarized glasses present different images to each eye
• Communication Systems: Satellite and radio signals use circular polarization
• Microscopy: Improves imaging of biological tissues
• LCDs: Work by controlling the state of polarization
• Chirality Analysis: Used in biochemistry to study optical activity

✦ Summary

Elliptical and circular polarization are complex but essential aspects of light behavior. They result from combining two linear components with a phase shift and are widely used in both science and industry.

Quarter Wave and Half Wave Plates

✦ Introduction

Wave plates (retarders) are optical devices made from birefringent materials that introduce a phase shift between two orthogonal components of polarized light. The two most common types are:

• Quarter Wave Plate (λ/4): Introduces a 90° phase shift
• Half Wave Plate (λ/2): Introduces a 180° phase shift

✦ Working Principle

Light entering a birefringent material splits into an ordinary and extraordinary ray. These rays travel at different velocities, resulting in a phase shift.

δ = (2π d (no - ne)) / λ

Where δ = phase difference, d = thickness of the plate, and n_o, n_e are refractive indices.

✦ Quarter Wave Plate (λ/4)

• Introduces a 90° (π/2) phase shift
• Converts linearly polarized light into circular or elliptical
• If light is incident at 45°, output becomes circularly polarized
• Used in 3D glasses, microscopy, optical analysis

✦ Half Wave Plate (λ/2)

• Introduces a 180° (π) phase shift
• Rotates the plane of polarization of linearly polarized light
• Converts right-handed circular to left-handed circular and vice versa
• Used in lasers, polarimetry, and communication systems

✦ Applications

• Laser Optics: Rotate and align polarization
• 3D Display Systems: Create circular polarization
• Microscopy: Enhance specimen visibility
• Communication: Polarization modulation in fiber optics
• Vision Science: Analyze corneal birefringence

✦ Summary

Quarter and half wave plates are vital tools in optical science for modifying the polarization state of light. They are widely used in scientific instruments, display technologies, and vision research.

Polaroids and Their Uses

✦ Introduction

Polaroids are optical filters made of special materials that allow only light vibrating in one direction to pass through. They convert unpolarized light into plane-polarized light and are widely used in modern optical and vision technologies.

✦ Structure of a Polaroid

• Made from stretched polyvinyl alcohol (PVA) chains.
• Doped with iodine or dichroic dyes that absorb light polarized along the chain direction.
• Allow transmission of light polarized perpendicular to the chains.

✦ Working Principle

When unpolarized light passes through a Polaroid:

• Vibrations aligned with the polymer chains are absorbed.
• Vibrations perpendicular to the chains are transmitted.

This results in linearly polarized light.

✦ Types of Polaroids

• H-Sheet: Iodine-doped PVA; common in eyewear and photography.
• K-Sheet: Dichroic dye-based; more durable and stable.
• Wire-Grid: Nanowire arrays used for infrared/microwave applications.

✦ Advantages

• Lightweight and flexible
• Cost-effective
• Efficient across visible wavelengths
• Easy to laminate onto lenses or screens

✦ Applications

• Sunglasses: Reduce glare and enhance visual comfort.
• Photography: Remove reflections and improve contrast.
• 3D Glasses: Used for separate image delivery to each eye.
• LCD Screens: Use two Polaroid sheets to control pixel illumination.
• Scientific Instruments: Polarimeters, polarizing microscopes, stress analysis tools.
• Optical Communication: Modulate and filter polarized light signals.

✦ Summary

Polaroids have revolutionized the use of polarized light in optical applications. From eyewear to electronics and scientific instruments, their affordability and effectiveness make them an indispensable tool in applied optics and optometry.

Optical Activity

✦ Introduction

Optical activity is the ability of certain substances to rotate the plane of polarization of light passing through them. This phenomenon is a result of chiral (asymmetric) molecular structures and is widely used in chemistry, biology, and vision science.

✦ Causes of Optical Activity

Optical activity is caused by the interaction of light with chiral molecules that exhibit different behaviors for left and right circularly polarized components, resulting in net rotation of linearly polarized light.

✦ Types of Optically Active Substances

• Natural Substances: Sucrose, glucose, tartaric acid, essential oils
• Crystalline Substances: Quartz and other chiral crystals

✦ Dextro and Levo Rotatory

• Dextrorotatory (D or +): Rotate polarization clockwise (e.g., sucrose)
• Levorotatory (L or −): Rotate polarization counterclockwise (e.g., fructose)

✦ Measuring Optical Rotation

α = [α] × c × l

• α = angle of rotation (degrees)
• [α] = specific rotation
• c = concentration in g/cm³
• l = length in decimeters

✦ Instruments Used

• Polarimeter: Device to measure the rotation angle of polarized light
• Laurent’s Half-Shade, Bi-quartz, Digital Polarimeters

✦ Applications

• Pharmaceuticals: Drug purity and enantiomer analysis
• Food Industry: Sugar content determination
• Biochemistry: Analyzing amino acids, proteins, sugars
• Optometry: Lens material and ocular fluid studies
• Chemical Testing: Identifying unknown chiral substances

✦ Summary

Optical activity demonstrates how polarized light interacts with molecular structure. It's a valuable property for analyzing chemical composition, monitoring drug quality, and understanding biological molecules. Instruments like polarimeters make precise measurements possible.

Fresnel’s Explanation of Optical Activity

✦ Introduction

Augustin-Jean Fresnel provided a wave-theory-based explanation of optical activity. He showed that optically active substances rotate the plane of polarized light because they affect left and right circularly polarized components differently.

✦ Key Idea

• Linearly polarized light = combination of right and left circularly polarized waves
• In optically active media, these components travel at different speeds
• This causes a phase shift and rotation of the resulting linear polarization

✦ Fresnel’s Model

1. Decomposition: Linear light splits into RCP and LCP components
2. Propagation: RCP and LCP travel at different velocities → phase difference
3. Recombination: The exit wave is linearly polarized but rotated

✦ Mathematical Relation

θ = (π × l × (nL - nR)) / λ

• θ: Rotation angle
• n_L and n_R: Refractive indices for LCP and RCP waves
• l: Length of the optically active medium
• λ: Wavelength of light

✦ Significance

• Connects optical activity with circular birefringence
• Explains why rotation depends on wavelength and path length
• Lays foundation for polarimetric instruments

✦ Applications

• Polarimeters: Measure optical rotation using Fresnel’s principles
• Optical Rotators: Devices that rotate polarization in fiber optics
• Chirality Analysis: Studying molecules in pharmaceuticals and biology
• Gyroscopes and Optical Circuits: Use circular birefringence in sensors

✦ Summary

Fresnel’s theory revealed the mechanism of optical activity as a result of unequal propagation of left and right circularly polarized waves. His wave-based explanation is crucial in understanding and designing optical systems involving polarization rotation.

Bi-Quartz Polarimeter

✦ Introduction

A Bi-quartz polarimeter is an optical instrument used to measure the rotation of polarized light by optically active substances. It uses two quartz semicircles that rotate light in opposite directions, enhancing the sensitivity and accuracy of rotation detection.

✦ Principle

• Plane-polarized white light passes through two semicircular quartz plates.
• One half rotates light clockwise (dextro-quartz), the other counterclockwise (levo-quartz).
• When no optically active substance is present, both halves appear the same color.
• Adding an optically active solution causes unequal rotation → color difference appears.
• Analyzer is rotated until both halves appear identical again → angle gives optical rotation.

✦ Construction

• Light Source: White or sodium light
• Polarizer: Produces plane-polarized light
• Bi-quartz Plate: Two fused semicircular plates
• Sample Tube: Holds optically active liquid
• Analyzer: Rotatable to measure angle
• Telescope: For observing colored fields

✦ Advantages

• High sensitivity to small rotations
• Color contrast enhances visibility of rotation
• Works with white light
• Simple and cost-effective

✦ Applications

• Sugar Industry: Measure concentration in cane juice or syrup
• Pharmaceuticals: Verify concentration and purity of chiral compounds
• Chemical Analysis: Identify optically active substances
• Education: Demonstration of polarization and rotation

✦ Summary

The Bi-quartz polarimeter uses the interaction of polarized light with optically active substances to measure rotation accurately. Its use of opposing quartz plates and color contrast provides a practical and visual way to understand and quantify optical activity.

Determination of Specific Rotatory Power (Half-Shade Polarimeter)

✦ Introduction

Specific rotatory power is a fundamental property of optically active substances, indicating how much they rotate plane-polarized light. It is measured using a Half-Shade Polarimeter, commonly employed in sugar analysis and pharmaceutical testing.

✦ Definition

[α] = α / (l × c)

• [α]: Specific rotatory power (°·dm⁻¹·g⁻¹·cm³)
• α: Observed rotation (degrees)
• l: Length of sample tube in decimeters
• c: Concentration in g/cm³

✦ Principle of Half-Shade Polarimeter

• Consists of a half-glass, half-quartz plate to create two slightly out-of-phase fields
• Equal brightness = no optical rotation
• Optically active solution rotates light → unequal brightness
• Analyzer is rotated until both halves match again → angle measured

✦ Construction

• Light Source: Monochromatic sodium light
• Polarizer: Creates polarized light
• Half-Shade Device: Provides visual sensitivity
• Sample Tube: Holds the test solution
• Analyzer: Measures the angle of rotation
• Scale and Eyepiece: For reading and observation

✦ Procedure

1. Fill sample tube with solution
2. Align polarizer and analyzer for equal brightness (baseline)
3. Insert tube → rotation occurs
4. Adjust analyzer to restore brightness match
5. Read angle and calculate [α] using formula

✦ Applications

• Sugar Industry: Determine sucrose concentration
• Pharmaceuticals: Test optical purity of chiral drugs
• Biochemistry: Analyze amino acids and glucose
• Academic Use: Demonstrate optical rotation principles

✦ Summary

The Half-Shade Polarimeter is an accurate and visual method for measuring optical rotation. Its use of brightness comparison enables precise determination of specific rotatory power, vital in chemical and biological studies.

Fluorescence and Phosphorescence

✦ Introduction

Fluorescence and phosphorescence are types of luminescence—light emitted by a substance without heating. They involve absorption of light and re-emission at a longer wavelength, but differ in duration and mechanism.

✦ Fluorescence

• Definition: Immediate emission of light upon UV/visible light absorption
• Duration: Very short (10⁻⁹ to 10⁻⁷ seconds)
• Mechanism: Excitation to singlet state, followed by return to ground state
• Examples: Fluorescein dye, detergents, highlighters

✦ Phosphorescence

• Definition: Delayed emission of light, continues after light source is removed
• Duration: Long (microseconds to hours)
• Mechanism: Transition via triplet state (forbidden transition)
• Examples: Glow-in-the-dark stickers, strontium aluminate

✦ Comparison Table

Property	Fluorescence	Phosphorescence
Electron State	Singlet	Triplet
Emission Duration	Nanoseconds	Seconds to hours
After Glow	No	Yes
Transition Type	Allowed	Forbidden
Examples	Fluorescein, whitening agents	Glow paints, luminous watches

✦ Applications

• Optometry: Fluorescein dye test for corneal assessment
• Biology: Staining tissues in fluorescent microscopy
• Forensics: Detect bodily fluids using UV light
• Security: Anti-counterfeit inks
• Consumer Products: Glow-in-the-dark materials and lighting

✦ Summary

Fluorescence is fast and stops instantly after excitation, while phosphorescence lingers. Both are crucial in optometry, diagnostics, security, and product design.

Click for more units of physical optics 👇

👉 Unit 1 Nature of light (part 1)

👉 Unit 1 Source of light (part 2)

👉 Unit 2 Interference of Light 

👉 Unit 3 Diffraction and Scattering 

👉 Unit 4 Polarization of Light 

👉 Unit 5 LASERS