Why can longitudinal waves, such as sound, not be polarised?

Longitudinal waves oscillate parallel to the direction of energy transfer. Since there is only one possible direction of oscillation (the axis of travel), there are no alternative planes to filter or restrict.

What is the difference between a polariser and an analyser?

A polariser is used to convert unpolarised light into plane-polarised light. An analyser is a second polarising filter used to determine the orientation or degree of polarisation of the light incident upon it.

How does the intensity of unpolarised light change after passing through a single ideal polarising filter?

The intensity is reduced by exactly 50% ($I = \frac{1}{2} I_0$). This is because the filter only transmits the components of the randomly oriented electric fields that are parallel to its transmission axis.

What is a common mistake when applying Malus's Law to intensity calculations?

Forgetting to square the cosine of the angle. Since intensity is proportional to the square of the amplitude ($I \propto A^2$), the formula must be $I = I_0 \cos^2 \theta$.

What error occurs if you assume the angle $\theta$ in Malus's Law is measured from the horizontal?

The angle $\theta$ must be the angle between the plane of polarisation of the incident light and the transmission axis of the filter. Using an arbitrary reference like the horizontal will lead to incorrect intensity values.

Why is it incorrect to say that a polariser 'creates' light energy?

A polariser is a passive component that filters out (absorbs) energy from unwanted planes of oscillation. It always reduces the total energy/intensity of the light beam; it never increases it.

Define 'Plane of Vibration'.

The plane of vibration is the single plane in which the electric field of a plane-polarised electromagnetic wave oscillates.

What is the 'Transmission Axis' of a polaroid?

The transmission axis is the specific direction within a polarising filter that allows the electric field component of a light wave to pass through with minimal absorption.

State the relationship between Intensity ($I$) and Amplitude ($A$).

Intensity is directly proportional to the square of the amplitude ($I \propto A^2$). This relationship explains why filtering the amplitude by $\cos \theta$ results in an intensity reduction of $\cos^2 \theta$.

Malus's Law states that the intensity $I$ of plane-polarised light transmitted through a polariser is $I = I_0 \cos^2 \theta$, where $I_0$ is the incident intensity and $\theta$ is the angle between the light's polarisation plane and the filter's axis.

Plane Polarisation | Pearson Edexcel AS-Level Physics

5. Waves & Particle Nature of Light

Plane Polarisation

Summary

Plane polarisation is a phenomenon exclusive to transverse waves where the oscillations of the wave are restricted to a single plane perpendicular to the direction of energy transfer. This process serves as definitive evidence for the transverse nature of electromagnetic waves, such as light, distinguishing them from longitudinal waves which cannot be polarised.

1. Definition & Core Concepts

Unpolarised light consists of transverse electromagnetic waves where the electric field vector oscillates in all possible planes perpendicular to the direction of propagation.

Plane polarisation occurs when these oscillations are restricted to a single, fixed plane, known as the plane of vibration.

The plane of polarisation is defined as the plane containing the direction of propagation and the direction of the electric field oscillations.

Only transverse waves can be polarised because their oscillations occur perpendicular to the direction of travel; longitudinal waves (like sound) oscillate parallel to travel and thus have no 'planes' to restrict.

Diagram showing unpolarised light with multiple oscillation planes passing through a vertical polarising filter to emerge as vertically plane-polarised light.

2. Underlying Principles

3. Methods of Production

Polarising Filters (Polaroids): These materials contain long-chain molecules aligned in one direction. They absorb light oscillating in one plane and transmit light oscillating in the perpendicular plane.

Reflection: When unpolarised light reflects off a non-metallic surface (like water or glass), the reflected ray becomes partially or completely plane-polarised parallel to the surface.

Scattering: Light scattered by small particles (like molecules in the atmosphere) can become polarised. This is why the blue sky appears polarised when viewed at certain angles relative to the sun.

4. Key Distinctions

Unpolarised vs. Polarised: Unpolarised light has oscillations in infinite planes; polarised light has oscillations in exactly one plane.
Polariser vs. Analyser: A 'polariser' is the first filter used to create polarised light; an 'analyser' is a second filter used to detect or measure the polarisation of that light.

Feature	Transverse Waves	Longitudinal Waves
Oscillation Direction	Perpendicular to travel	Parallel to travel
Polarisation Possible?	Yes	No
Example	Light, S-waves	Sound, P-waves

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

Plane Polarisation

Summary

1. Definition & Core Concepts

Unpolarised light consists of transverse electromagnetic waves where the electric field vector oscillates in all possible planes perpendicular to the direction of propagation.

Plane polarisation occurs when these oscillations are restricted to a single, fixed plane, known as the plane of vibration.

The plane of polarisation is defined as the plane containing the direction of propagation and the direction of the electric field oscillations.

Diagram showing unpolarised light with multiple oscillation planes passing through a vertical polarising filter to emerge as vertically plane-polarised light.

2. Underlying Principles

The intensity of a wave is directly proportional to the square of its amplitude ( $I \propto A^2$ ). This relationship is fundamental to understanding how intensity changes during polarisation.

When unpolarised light passes through an ideal polariser, the intensity is reduced by half ( $I = \frac{1}{2} I_0$ ) because the filter only transmits the component of the electric field parallel to its transmission axis.

If the incident light is already plane-polarised, the transmitted amplitude depends on the angle $\theta$ between the light's plane of vibration and the filter's transmission axis, given by $A = A_0 \cos \theta$ .

Applying the intensity-amplitude relationship leads to Malus's Law, which states that the transmitted intensity $I$ is given by $I = I_0 \cos^2 \theta$ .

3. Methods of Production

Reflection: When unpolarised light reflects off a non-metallic surface (like water or glass), the reflected ray becomes partially or completely plane-polarised parallel to the surface.

4. Key Distinctions

Unpolarised vs. Polarised: Unpolarised light has oscillations in infinite planes; polarised light has oscillations in exactly one plane.
Polariser vs. Analyser: A 'polariser' is the first filter used to create polarised light; an 'analyser' is a second filter used to detect or measure the polarisation of that light.

Feature	Transverse Waves	Longitudinal Waves
Oscillation Direction	Perpendicular to travel	Parallel to travel
Polarisation Possible?	Yes	No
Example	Light, S-waves	Sound, P-waves

5. Exam Strategy & Tips

Identify Wave Type: If a question asks for proof that light is a transverse wave, the answer is always 'it can be polarised'.
Intensity Calculations: Always remember to square the cosine term when using Malus's Law ( $I = I_0 \cos^2 \theta$ ). A common mistake is using $I = I_0 \cos \theta$ .
Crossed Polarisers: If two polarisers are 'crossed' (at $90^\circ$ to each other), the transmitted intensity is zero because $\cos^2(90^\circ) = 0$ .
Sanity Check: The intensity of light after passing through a polariser can never be greater than the incident intensity.

6. Common Pitfalls & Misconceptions

Sound Polarisation: Students often mistakenly think sound can be polarised. Sound is longitudinal and cannot be restricted to a plane of oscillation perpendicular to its travel.
The 50% Rule: Many forget that the first polariser always reduces unpolarised light intensity by 50%, regardless of its orientation.
Plane of Polarisation vs. Vibration: Ensure you distinguish between the plane where the electric field oscillates (vibration) and the plane perpendicular to it (often used in older texts as the plane of polarisation).