Physics (9702) | Polarisation

Cambridge International AS & A Level Physics (9702): Study Notes on Polarisation

Hello future physicists! This chapter, Polarisation, is often seen as a short but tricky topic because it forces us to think carefully about the nature of waves. Don't worry, we'll break down these ideas using simple analogies.

In simple terms, Polarisation is proof that light (and all electromagnetic waves) are transverse waves. It explains why sunglasses work and why some light appears "glary." Mastering this section shows you truly understand wave behaviour!

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1. The Essential Prerequisite: Transverse Waves

1.1 Why Polarisation Only Affects Transverse Waves

The very first thing the syllabus requires you to know is the crucial link between polarisation and wave type.

Understanding Wave Motion

• Longitudinal Waves: The particles in the medium vibrate parallel to the direction the wave is travelling.
  Example: Sound waves.
• Transverse Waves: The particles in the medium vibrate perpendicular (at 90°) to the direction the wave is travelling.
  Example: Light waves, waves on a string.

Analogy Time: The Fence and the Rope
Imagine you shake a rope to create a wave, and you feed the rope through a vertical slit in a fence.

1. If you shake the rope up and down (vertical vibration), the wave passes through the vertical slit easily (Transverse motion).
2. If you shake the rope side to side (horizontal vibration), the wave hits the sides of the fence slit and cannot pass (Transverse motion blocked).
3. If you shake a long spring forward and backward (Longitudinal motion, like sound), the slit doesn't matter; the pulse still moves forward.

Key Takeaway (Syllabus Point 7.5.1): Since we can block certain vibrations of light (like the horizontal ones in the analogy), it proves that the vibrations must be perpendicular to the direction of travel. Therefore, polarisation is a phenomenon associated exclusively with transverse waves. Longitudinal waves cannot be polarised.

2. Defining Polarised and Unpolarised Light

2.1 Unpolarised Light

Most light we encounter—like sunlight or light from a normal lamp—is unpolarised.

• In unpolarised light, the electric field (which dictates the vibration direction) vibrates randomly in all possible planes perpendicular to the direction of wave travel.
• If you look down the ray, the vibrations are occurring in every direction—up/down, left/right, and all angles in between.

2.2 Plane-Polarised Light

Plane-Polarised Light (or linearly polarised light) is light where the vibrations of the electric field are restricted to just one single plane.

2.3 The Polarising Filter (The Polariser)

To get plane-polarised light, we use a filter called a polariser (often a Polaroid sheet).

This filter contains long chain molecules aligned in a specific direction. These molecules act like the vertical slit in our fence analogy:

1. When unpolarised light hits the polariser, only the component of the light vibrating parallel to the filter's transmission axis passes through.
2. The components vibrating perpendicular to the transmission axis are absorbed or reflected.
3. The resulting light is plane-polarised.

Quick Review: Intensity Reduction

Since unpolarised light contains equal components vibrating in all directions, when it passes through the first polarising filter (the polariser), roughly 50% of the energy (intensity) is absorbed.

BUT, remember the syllabus constraint: You are not required to calculate the intensity reduction of unpolarised light passing through the first filter. You just need to know it results in plane-polarised light with a reduced intensity, \(I_0\).

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3. Quantifying Polarisation: Malus's Law

Once we have plane-polarised light, what happens if we place a second filter in its path? This second filter is called the analyser. The amount of light that passes depends on the angle between the polariser and the analyser.

3.1 Setting up the Experiment

1. Light starts unpolarised.
2. It passes through the first filter (Polariser), becoming plane-polarised with initial intensity \(I_0\).
3. This polarised light \(I_0\) then hits the second filter (Analyser).
4. The angle \(\theta\) is the angle between the transmission axis of the Polariser and the transmission axis of the Analyser.

3.2 Malus's Law (Syllabus Point 7.5.2)

Malus's law calculates the final intensity \(I\) of the light transmitted through the analyser:

Formula: $$I = I_0 \cos^2\theta$$

• \(I\) is the final intensity of the light after passing through the analyser.
• \(I_0\) is the intensity of the *plane-polarised* light incident on the analyser (i.e., the light intensity after the first polariser).
• \(\theta\) is the angle between the transmission axes of the polariser and the analyser.

Don't worry if the \(\cos^2\theta\) part looks intimidating—it just means calculate the cosine of the angle first, and then square the result.

3.3 Step-by-Step Application of Malus's Law

The intensity of the light transmitted depends entirely on \(\cos^2\theta\). Let's look at the three most common scenarios:

1. Axes Parallel (\(\theta = 0^\circ\)): Maximum Transmission
   

   If the transmission axes of the polariser and analyser are parallel (aligned), \(\theta = 0^\circ\).
   \(\cos(0^\circ) = 1\), so \(\cos^2(0^\circ) = 1\).
   $$I = I_0 \times 1 = I_0$$

   Result: The maximum intensity passes through.

2. Axes Perpendicular (\(\theta = 90^\circ\)): Zero Transmission (Extinction)
   

   If the transmission axes are perpendicular (or "crossed"), \(\theta = 90^\circ\).
   \(\cos(90^\circ) = 0\), so \(\cos^2(90^\circ) = 0\).
   $$I = I_0 \times 0 = 0$$

   Result: No light passes through. This is called extinction, and it provides definitive proof of polarisation.

3. Axes at \(45^\circ\)
   

   If the angle is \(45^\circ\).
   \(\cos(45^\circ) \approx 0.707\).
   \(\cos^2(45^\circ) = 0.5\).
   $$I = I_0 \times 0.5 = 0.5 I_0$$

   Result: Half of the polarised light intensity passes through.

Common Mistake Alert!

Always ensure you use the angle \(\theta\) between the two transmission axes, not the angle of the light beam itself. And remember to square the cosine, not the angle!

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4. Real-World Applications of Polarisation

Polarisation isn't just a classroom concept; it has powerful everyday applications, primarily because light often becomes naturally polarised upon reflection.

4.1 Polarising Sunglasses

Glare from surfaces like water, glass, or roads is often horizontally plane-polarised.

• Polarising sunglasses have filters with vertical transmission axes.
• These vertical axes absorb the intense, horizontally polarised glare, significantly reducing brightness without making everything dark.

4.2 Photography

Photographers use polarising filters on camera lenses to:

• Darken the sky (light scattered by the atmosphere is partially polarised).
• Remove unwanted reflections from water or windows, allowing the camera to "see through" the glare.

4.3 3D Cinema

In older 3D cinemas, two projectors display two slightly different images.

• One image is projected using vertically polarised light.
• The other image is projected using horizontally polarised light.
• The viewer wears glasses containing two different filters (one vertical, one horizontal) so that each eye only sees its intended image, creating the 3D effect.

Did you know? Polarisation can also occur through scattering (like in the blue sky) and birefringence (splitting light in certain crystals). While these mechanisms are interesting, for your 9702 exam, the focus remains on understanding the link to transverse waves and applying Malus's Law to filter transmission.

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Summary: Core Concepts to Master

If you remember these two points, you have mastered the essentials of this chapter:

1. The Nature of Light: Polarisation only works because light is a transverse wave, meaning its electric field oscillates perpendicular to its path.

2. The Math of Filters: When plane-polarised light of intensity \(I_0\) passes through an analyser, the transmitted intensity \(I\) is governed by Malus's Law, \(I = I_0 \cos^2\theta\).

Great job! Now practice applying Malus's Law to those specific angles (\(0^\circ\), \(45^\circ\), \(90^\circ\)) and you’ll be set!