Polarisation - Physics (9478) - GCE A-Level - Higher 2 (H2)

Introduction to Polarisation

Hi there! Welcome to one of the most visual and "cool" chapters in Physics: Polarisation. Have you ever wondered how polarized sunglasses reduce glare while you're at the beach, or how 3D glasses at the cinema work? It all comes down to controlling the direction in which waves vibrate. Don't worry if waves feel a bit abstract right now—we’re going to break this down into simple, manageable steps using everyday analogies.

1. The Basics: What is Polarisation?

To understand polarisation, we first need a quick reminder about the two main types of waves:

1. Longitudinal Waves: Oscillations are parallel to the direction of energy transfer (like sound waves). Imagine pushing and pulling a Slinky spring.
2. Transverse Waves: Oscillations are perpendicular (at 90 degrees) to the direction of energy transfer (like light or ripples on a pond). Imagine shaking a rope up and down.

Crucial Point: Polarisation is a phenomenon that is only associated with transverse waves. Longitudinal waves cannot be polarised because they only vibrate in one line anyway!

What does "Polarised" mean?

In a normal beam of light (unpolarised light), the electromagnetic fields are vibrating in all possible directions perpendicular to the path of the wave. When we "polarise" the light, we use a filter to restrict those vibrations to just one single plane. This result is called plane-polarised light.

The "Picket Fence" Analogy

Imagine you have a rope passed through the gaps in a vertical picket fence. If you shake the rope up and down (vertically), the wave passes through easily. However, if you try to shake the rope side-to-side (horizontally), the fence blocks the motion. The fence acts as a polariser, only allowing the vertical "plane" of vibration to pass through.

Quick Review Box:
• Unpolarised: Vibrations in many planes.
• Plane-polarised: Vibrations restricted to one plane.
• Only transverse waves can be polarised.

Key Takeaway: Polarisation is the process of confining the oscillations of a transverse wave to a single plane.

2. Polarising Filters and Intensity

How do we actually do this in a lab? We use a polarising filter (often called a "Polaroid"). These filters contain long-chain molecules aligned in a specific direction. They only allow light vibrating in one specific direction—the transmission axis—to pass through.

What happens to Intensity?

When unpolarised light passes through a single polarising filter, exactly half of its intensity is lost.
If the incident unpolarised light has intensity \( I_{unpol} \), the transmitted polarised light has intensity:
\( I = \frac{1}{2} I_{unpol} \)

Did you know? This is why the world looks a bit darker when you put on polarised sunglasses! They are literally cutting out half of the light and even more of the reflected glare.

3. Malus’ Law: Predicting the Brightness

This is the "math part," but it's very logical! Malus’ Law helps us calculate what happens when light that is already polarised hits a second filter (often called an analyser).

If the first filter polarises the light, and then we place a second filter at an angle \( \theta \) to the first one, the transmitted intensity \( I \) is given by:

\( I = I_0 \cos^2\theta \)

Where:
• \( I_0 \) is the intensity of the light after it has passed through the first filter (the incident polarised light).
• \( \theta \) is the angle between the transmission axis of the first filter and the second filter.

Step-by-Step Breakdown of Malus' Law:

1. When \( \theta = 0^\circ \): The axes are parallel. \( \cos(0) = 1 \), so \( I = I_0 \). All the light passes through.
2. When \( \theta = 90^\circ \): The axes are "crossed" (perpendicular). \( \cos(90) = 0 \), so \( I = 0 \). No light passes through! This is called total extinction.
3. When \( \theta = 45^\circ \): \( \cos(45) = \frac{1}{\sqrt{2}} \). When you square it, you get \( \frac{1}{2} \). So, \( I = 0.5 I_0 \).

Amplitude and Malus' Law

Remember from the "Wave Motion" basics that Intensity is proportional to the square of the Amplitude (\( I \propto A^2 \)).
While the Intensity follows a \( \cos^2\theta \) relationship, the Amplitude \( A \) of the wave after the filter follows a simple cosine relationship:
\( A = A_0 \cos\theta \)

Common Mistake to Avoid: When using Malus' Law, always make sure your calculator is in Degrees (unless the angle is given in radians). Also, remember that \( I_0 \) is the intensity of the polarised light hitting the filter, not the original unpolarised source!

Key Takeaway: Malus’ Law (\( I = I_0 \cos^2\theta \)) relates the transmitted intensity to the angle between the light's plane of polarisation and the filter's transmission axis.

4. Summary and Practical Tips

Summary Table

Memory Aid: The "C.A.S." Trick

When solving problems, remember: Cosine for Amplitude, Square for Intensity.
\( A \propto \cos\theta \)
\( I \propto \cos^2\theta \)

Encouragement Corner

Don't worry if this seems tricky at first! The most common hurdle is simply remembering to square the cosine. Just keep the "picket fence" image in your head. If the slot is vertical and the wave is horizontal, nothing gets through!

Final Quick Review:
1. Is it a transverse wave? Yes? Then it can be polarised.
2. Is the light unpolarised? The first filter makes it \( \frac{1}{2} I \).
3. Is there a second filter? Use \( I = I_0 \cos^2\theta \).
4. Check the question: Are they asking for Intensity or Amplitude?

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