Malus's law Cambridge International AS & A Level Physics revision
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In plain words
Send polarised light through a polarising filter, and how much gets through depends on the angle between them. Lined up, all of it. Crossed, none. In between, a neat cos² rule gives the fraction.
Three things to know
- Malus's law: when plane-polarised light of intensity I₀ meets a polarising filter whose axis is at angle θ to the light's plane of polarisation, the transmitted intensity is I = I₀ cos²θ.
- The filter passes only the part of the amplitude that lies along its axis, A cos θ. Intensity depends on amplitude squared, which is where the cos² comes from.
- The light that comes out is polarised along the filter's axis. For a row of filters, apply the law one filter at a time, using the angle between each filter and the one before it.
Worked example
Plane-polarised light of intensity I₀ meets a polarising filter whose axis is at 60° to the light's plane of polarisation. Find the transmitted intensity.
- I = I₀ cos²θ.
- cos 60° = 0.50, so cos²60° = 0.25.
- I = 0.25 I₀.
Tips and tricks
- cos²θ means (cos θ)²: find the cosine first, then square it.
- θ is the angle between the plane of polarisation and the filter's axis. Lined up is 0°, not 90°.
It lands in your notebook with its questions as flashcards.
Malus's law: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Polarised light meets a filter at 90° to its plane of polarisation. How much gets through?
cos²90° = 0.
Polarised light of intensity I₀ meets a filter at 45°. What is the transmitted intensity?
cos²45° = 0.50.
Polarised light meets a filter whose axis is lined up with its plane of polarisation. How much gets through?
cos²0° = 1.
Polarised light of amplitude A meets a filter at angle θ. What amplitude is transmitted?
The filter passes the component along its axis. Squaring gives the intensity.
Polarised light of intensity 10 W/m² meets a filter at 60°. What is the transmitted intensity?
10 × cos²60°.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Malus's law
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
Polarised light meets a filter at 30° to its plane of polarisation. Find the fraction of the intensity transmitted.[2]
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0.75. cos²30°.
Polarised light of intensity 8.0 W/m² passes through a filter at 45° to its plane of polarisation, and then through a second filter at 45° to the first. Find the final intensity.[3]
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2.0 W/m². 8.0 × cos²45° = 4.0 W/m², then 4.0 × cos²45° = 2.0 W/m².
Find the angle at which half the intensity of polarised light is transmitted by a filter.[2]
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45°. cos²θ = 0.50.
Answers: Malus's law
- 1. 0.75. cos²30°.
- 2. 2.0 W/m². 8.0 × cos²45° = 4.0 W/m², then 4.0 × cos²45° = 2.0 W/m².
- 3. 45°. cos²θ = 0.50.