Polarisation

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand that polarisation is a phenomenon associated with transverse waves
  2. Recall and use Malus's law (I = I₀ cos² θ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters

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What is Polarisation?

Polarisation is a way of restricting the vibrations of a wave so they happen in only one direction (one plane). Think of it like forcing a rope wave to wiggle only up-and-down instead of in all directions.

Important: Only transverse waves can be polarised. Longitudinal waves cannot be polarised.

Let me explain why:

  • Transverse waves vibrate perpendicular (at right angles) to the direction the wave is traveling. For example, light waves or waves on a rope.
  • Because transverse waves can vibrate in any plane perpendicular to their direction of travel, we can restrict these vibrations to just one plane - this is polarisation.
  • Longitudinal waves (like sound waves) vibrate parallel to the direction of travel. They only vibrate back and forth along one line already, so there's nothing to restrict - they can't be polarised.

Unpolarised vs Polarised Waves

Unpolarised waves oscillate (vibrate) in many different planes at once. Imagine looking at a wave coming towards you - if it's unpolarised, it's vibrating in all directions around the direction of travel (up, down, left, right, and everything in between).

Polarised waves oscillate in only one plane. For example:

  • Vertically polarised - vibrates only in the vertical plane (up and down)
  • Horizontally polarised - vibrates only in the horizontal plane (left and right)

Even though the wave is restricted to one plane, it still travels perpendicular to that vibration direction.

Electromagnetic Waves and Polarisation

Electromagnetic waves (like light) are transverse waves made of two parts:

  • An electric field that oscillates in one plane
  • A magnetic field that oscillates in another plane
  • These two planes are perpendicular (at right angles) to each other
  • Both are perpendicular to the direction the wave travels

Natural light (like sunlight or light from a bulb) is unpolarised - it contains waves vibrating in all possible planes.

Polarising Filters (Polarisers)

A polarising filter (or polariser) is a special material that only allows waves vibrating in one particular direction to pass through.

How it works:

  • The filter acts like a grid of tiny parallel slits
  • Only waves vibrating parallel to these slits can pass through
  • Waves vibrating in other directions are blocked (absorbed)

Example: If you have a polariser with vertical slits:

  • Only vertically vibrating waves pass through
  • Horizontally vibrating waves are completely blocked
  • The light that comes out is vertically polarised

Malus's Law

When polarised light passes through a second polarising filter (called an analyser), the intensity of light that comes out depends on the angle between the two filters.

Malus's Law tells us this relationship:

I=I0cos⁡2θI = I_0 \cos^2 \theta

Where:

  • I = intensity of light transmitted through the analyser (in W m⁻²)
  • I₀ = intensity of polarised light before it hits the analyser (in W m⁻²)
  • θ = angle between the transmission axis of the polariser and the analyser (in degrees)

What this means in practice:

  1. When θ = 0° (filters aligned in the same direction):

    • cos²(0°) = 1
    • I = I₀
    • All the light passes through - maximum intensity

  2. When θ = 90° (filters perpendicular to each other):

    • cos²(90°) = 0
    • I = 0
    • No light passes through - complete darkness

  3. When θ = 30°:

    • cos²(30°) = 0.75
    • I = 0.75 I₀
    • 75% of the light intensity passes through

Using Malus's Law with Multiple Filters

When unpolarised light passes through multiple filters:

Step 1: When unpolarised light first passes through a polariser, it becomes polarised. The intensity after the first filter is I₀.

Step 2: Apply Malus's law for each additional filter (analyser), using the angle between consecutive filters.

Important note: The angle θ in Malus's law is the angle between the transmission axes of consecutive filters, not the angle from some fixed reference point.

Worked Example: Two Filters

Question: Polarised light with intensity I₀ passes through a polarising filter. The filter is oriented at 30° to the direction of polarisation. What is the transmitted intensity?

Solution:

  • Use Malus's law: I = I₀ cos² θ
  • θ = 30°
  • I = I₀ cos²(30°)
  • I = I₀ × (√3/2)²
  • I = I₀ × 3/4
  • I = 0.75 I₀

The transmitted intensity is 75% of the original intensity.

Worked Example: Multiple Filters in Series

Question: Polarised light passes through two analysers. The first analyser is at 20° to the original polarisation direction. The second analyser is at 50° to the original polarisation direction. If the initial intensity is I₀, what is the final intensity?

Solution:

Step 1: Light passes through first analyser at 20°

  • I₁ = I₀ cos²(20°)
  • I₁ = I₀ × 0.883
  • I₁ = 0.883 I₀

Step 2: Light passes through second analyser

  • The angle between the two analysers is: 50° - 20° = 30°
  • I₂ = I₁ cos²(30°)
  • I₂ = 0.883 I₀ × 0.75
  • I₂ = 0.66 I₀

The final transmitted intensity is 66% of the original intensity.

Application: Polaroid Sunglasses

Polaroid sunglasses are a practical application of polarisation:

  • The lenses contain polarising filters with vertical transmission axes
  • Light reflected from horizontal surfaces (like water or roads) becomes horizontally polarised
  • The vertical filters in the sunglasses block this horizontally polarised glare
  • Only vertically polarised light passes through
  • This reduces glare and makes it easier to see

This is why Polaroid sunglasses are especially useful near water or while driving - they cut out the reflected glare that ordinary sunglasses cannot block as effectively.

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