Class 12/Notes/Wave Optics
1.Introduction: Why Can Light Be Polarised?
Light is an electromagnetic wave in which the electric field and magnetic field oscillate perpendicular to the direction of propagation.
The vibrations of the electric field can be restricted to a particular direction.
This phenomenon is called polarisation of light.
Polarisation provides one of the strongest pieces of evidence that light is a transverse wave.
Exam Alert: Longitudinal waves cannot be polarised. Therefore, the phenomenon of polarisation establishes the transverse nature of light.
2. What is Polarisation of Light?
Polarisation is the phenomenon of restricting the vibrations of the electric field of a transverse light wave to a particular direction perpendicular to its direction of propagation.
Consider a light wave travelling along the x-axis.
In ordinary light, the electric field can vibrate in many directions in the plane perpendicular to the direction of propagation.
After polarisation, the vibrations are restricted to one particular direction.
Unpolarised Light
In ordinary or unpolarised light:
- Electric-field vibrations occur in many directions.
- These directions are perpendicular to the direction of propagation.
- There is no single preferred direction of vibration.
Plane-Polarised Light
In plane-polarised light:
- The electric field vibrates in only one direction.
- The vibration direction is perpendicular to the direction of propagation.
- The light is said to be linearly or plane polarised.
3. Unpolarised Light vs Plane-Polarised Light
| Feature | Unpolarised Light | Plane-Polarised Light |
| Direction of propagation | Fixed | Fixed |
| Direction of electric-field vibration | Many directions | One fixed direction |
| Preferred vibration direction | Absent | Present |
| Can be produced using a polariser? | — | Yes |
| Nature of wave | Transverse | Transverse |
| Example | Sunlight, ordinary bulb light | Light emerging from a Polaroid |
4. Types of Polarisations
Polarisation can occur in different forms depending on how the electric-field vector behaves with time.
Major types
- Linear or Plane Polarisation
- Circular Polarisation
- Elliptical Polarisation
4.1 Linear or Plane Polarisation
The electric field oscillates along a fixed direction while the wave propagates.
The tip of the electric-field vector traces a straight line.
This is the most commonly discussed form of polarisation in school-level optics.
4.2 Circular Polarisation
In circular polarisation, the magnitude of the electric field remains constant, but its direction continuously rotates.
The tip of the electric-field vector traces a circle.
Circular polarisation can be produced by introducing an appropriate phase difference between two mutually perpendicular components of the electric field.
4.3 Elliptical Polarisation
In elliptical polarisation, the tip of the electric-field vector traces an ellipse.
It is the more general state of polarisation.
Conceptual Relationship
Linear polarisation → straight line
Circular polarisation → circle
Elliptical polarisation → ellipse
5. How is Polarised Light Produced?
Polarised light can be produced by several methods.
The important methods are:
1. Polarisation by Reflection
When unpolarised light is reflected from a transparent surface at a particular angle, the reflected light becomes completely plane polarised.
This leads to Brewster’s law.
2. Polarisation by Refraction
The transmitted/refracted light can become partially polarised when light passes through a transparent medium.
3. Polarisation by Double Refraction
Certain anisotropic crystals can split light into two refracted rays with different polarisation properties.
4. Polarisation by Selective Absorption
Materials such as Polaroids selectively absorb vibrations in one direction and transmit vibrations perpendicular to it.
6. Polaroid: A Simple Polarising Device
A Polaroid is a material that transmits light vibrations predominantly along one particular direction while absorbing the perpendicular component.
The direction in which vibrations are transmitted is called the transmission axis.
When unpolarised light passes through a Polaroid, the emerging light is plane polarised.
7. Polariser and Analyzer
Two Polaroids can be used to study the behaviour of polarised light.
Polariser
The first Polaroid converts unpolarised light into plane-polarised light.
Analyzer
The second Polaroid is used to examine the polarisation state of the light.
The angle between their transmission axes is called θ.
This arrangement forms the basis of Malus’ law.
8. Malus’ Law
Malus’ law describes the intensity of plane-polarised light transmitted through an analyser.
If plane-polarised light of intensity I₀ is incident on an analyser whose transmission axis makes an angle θ with the direction of polarisation, then:
I = I₀ cos² θ
where:
- I₀ = intensity of incident plane-polarised light
- I = intensity transmitted by the analyser
- θ = angle between the transmission axes of the polariser and analyser
9. Derivation of Malus’ Law
Suppose the amplitude of the electric field of incident plane-polarised light is E₀.
The analyser allows only the component of the electric field along its transmission axis to pass.
Therefore:
E = E₀ cos θ
Since intensity is proportional to the square of amplitude:
I ∝ E²
Therefore:
I / I₀ = cos² θ
Hence:
I = I₀ cos² θ
This is Malus’ law.
10. Special Cases of Malus’ Law
These cases are extremely important for NEET and JEE.
Case 1: Parallel Polaroids
If:
θ = 0°
Then:
I = I₀
Maximum intensity is transmitted.
Case 2: Crossed Polaroids
If:
θ = 90°
Then:
I = 0
No light passes through the analyser, assuming ideal Polaroids.
This arrangement is called crossed Polaroids.
Case 3: θ = 60°
Since:
cos 60° = 1/2
Therefore:
I = I₀/4
Only one-fourth of the incident plane-polarised intensity is transmitted.
Case 4: θ = 45°
Since:
cos 45° = 1/√2
Therefore:
I = I₀/2
Half of the incident plane-polarised intensity is transmitted.
11. Malus’ Law: High-Yield Formula Box
Malus’ Law
I = I₀ cos² θ
Remember:
- θ = 0° → I = I₀
- θ = 45° → I = I₀/2
- θ = 60° → I = I₀/4
- θ = 90° → I = 0
NEET Shortcut
Whenever the question gives the angle between the transmission axes of the polariser and analyser, immediately think:
I = I₀ cos² θ
11. Polarisation by Reflection
When unpolarised light reflects from a dielectric surface (glass, water), the reflected light becomes partially polarised. At a specific angle, it becomes completely plane polarised.
Observations:
- The reflected light has its electric field perpendicular to the plane of incidence (s-polarised).
- The refracted light is partially polarised with a component parallel to the plane of incidence (p-polarised).
- At Brewster’s angle, the reflected and refracted rays are perpendicular to each other.
Explanation:
At Brewster’s angle, the electric dipoles in the medium oscillate in the direction of the refracted ray. Since the reflected ray is perpendicular to the refracted ray, the dipoles cannot radiate in the direction of the reflected ray for the p-component. Hence, only the s-component is reflected.
12. Brewster’s Angle and Geometry
At the Brewster angle:
iₚ + r = 90°
Therefore:
The reflected ray and refracted ray are mutually perpendicular.
This is a highly important CBSE derivation and JEE conceptual result.
Using Snell’s law: μ = sin iₚ / sin r
Since: r = 90° − iₚ
we get: sin r = cos iₚ
Therefore: r = 90° − iₚ
Hence: μ = tan iₚ
This is Brewster’s law.
Applications:
- Polarising sunglasses reduce glare from horizontal surfaces (water, roads) — glare is horizontally polarised (s-polarised relative to the surface).
- Brewster windows in lasers to produce polarised output.
- Photography: polarising filters to darken skies and reduce reflections
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