Apply polarisation and Malus’s law
Explain why polarisation identifies transverse waves and calculate transmitted intensity with Malus's law.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 7. These original wave examples and diagrams are conceptual study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use frequency, period, wavelength, amplitude, speed and trigonometric ratios with consistent units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What kind of wave can be polarised?
What you will learn
- Relate polarisation to transverse oscillations
- Use Malus's law for plane-polarised electromagnetic waves
- Calculate intensity after one or more polarising filters
Polarisation selects an oscillation direction
Polarisation is a phenomenon associated with transverse waves. A polarising filter transmits the component of a wave's oscillation aligned with its transmission axis and blocks the perpendicular component.
A longitudinal oscillation is parallel to propagation and has no transverse direction to select in this way. Observing polarisation therefore provides evidence that the wave is transverse.
Use Malus's law for plane-polarised input
For plane-polarised electromagnetic waves incident on a filter, Malus's law gives I = I₀ cos²θ, where θ is the angle between the incident plane of polarisation and the filter's transmission axis.
For a sequence of filters, apply the law at each step using the intensity arriving at that filter and the relative angle between the current polarisation and its axis. This syllabus calculation starts with plane-polarised input; do not halve an unpolarised intensity unless a question specifically supplies a separate model.
Pause and explain
At what angle does a filter transmit zero intensity from plane-polarised input?
Worked example
Plane-polarised light of intensity 80 W m⁻² reaches a filter whose transmission axis is 60° to its polarisation. Find the transmitted intensity.
Show the worked solution
- Use I = I₀ cos²θ.
- cos 60° = 0.5, so cos²60° = 0.25.
- I = 80 × 0.25.
Answer 20 W m⁻².
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Plane-polarised radiation of intensity 50 W m⁻² passes through a filter at 0° to its polarisation. Find the transmitted intensity.
Give me a hint
At zero relative angle, cos²0° = 1.
Compare my reasoning
- I = I₀ cos²θ.
- I = 50 cos²0°.
- Evaluate the cosine factor.
50 W m⁻².
Look for these in your work
- Malus's law used
- Angle interpreted
- Intensity unit retained
Plane-polarised light with I₀ = 120 W m⁻² passes through a filter at 30°. Find the transmitted intensity.
Give me a hint
Use cos²30° = 3/4, then multiply the incoming intensity by that fraction.
Compare my reasoning
- I = 120 cos²30°.
- I = 120 × 0.75.
- Calculate in W m⁻².
90 W m⁻².
Look for these in your work
- Relative angle used
- Cosine squared
- Intensity calculated
Plane-polarised light of intensity 100 W m⁻² passes through two filters. The first axis is 60° from its polarisation; the second is 30° from the first axis. Find the final intensity.
Give me a hint
Apply Malus's law successively, using each transmitted intensity as the next I₀.
Compare my reasoning
- After filter 1: I₁ = 100 cos²60° = 25 W m⁻².
- The second relative angle is 30°, so I₂ = 25 cos²30°.
- I₂ = 25 × 0.75 = 18.75 W m⁻².
18.75 W m⁻² after both filters.
Look for these in your work
- First transmission calculated
- Relative angle between filters used
- Second transmission applied to I₁
Common mistakes
- Using cos θ rather than cos²θ
- Measuring θ from the propagation direction instead of the polarisation axis
- Applying this plane-polarised-input equation to an unspecified unpolarised input
What can you explain now?
What kind of wave can be polarised?
Compare with the explanation
A transverse wave
A transverse oscillation has an orientation that a filter can select.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
What does a polarising filter reveal about the orientation of a wave's oscillation?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.