The shape of the lesson
By the end of the lesson, learners can
- Two filters, one angle: Rotate the second polariser and watch the transmitted intensity follow I = I₀ cos²θ: bright when aligned, dark when crossed at 90°.
- Malus law: The transmitted intensity depends on the square of the cosine of the angle.
- Polarisation as evidence: That light polarises and sound does not is a clean test of wave type.
- Law: I = I₀ cos²θ.
- Crossed: 90° gives zero.
- Test: only transverse waves polarise.
One picture every idea returns to
Polarisation is the restriction of the oscillations of a transverse wave to a single plane; only transverse waves can be polarised. After a first polariser, a second polariser (the analyser) transmits an intensity given by Malus law, I = I₀ cos²θ, where θ is the angle between the transmission axes. At 90° (crossed) no light gets through.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Picking one plane.. A transverse wave can oscillate in any plane perpendicular to its travel. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Two filters, one angle | Rotate the second polariser and watch the transmitted intensity follow I = I₀ cos²θ: bright when aligned, dark when crossed at 90°. Project tab 5 of the lab (Polarisation) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Malus law | The transmitted intensity depends on the square of the cosine of the angle. | Pairs |
| 21 to 30 min | Teach and check: Polarisation as evidence | That light polarises and sound does not is a clean test of wave type. | Cooperative Concept Mapping |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Polarisation as evidence, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Cooperative Concept Mapping
Teams receive the key terms on cards and arrange them on a large sheet, drawing and labelling the links. Compare maps between teams before showing the model map.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Malus law uses cos squared, not cos: at 60° the transmitted fraction is cos²60° = 0.25, not 0.5. | The angle θ is measured between the transmission axes (equivalently between the light's polarisation and the analyser axis). And remember crossed polarisers (90°) give zero, the basis of many optical switches. |
Polarisation: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
State what is meant by saying that light is plane polarised.
Two ideal polarisers are placed with their transmission axes crossed at 90°. State the transmitted intensity and justify it with Malus law.
Plane polarised light of intensity I₀ passes through a polariser whose axis is at 45° to the polarisation. Find the transmitted intensity.
Plane polarised light meets a filter whose axis is at 20° to the light's polarisation. Find the fraction of the intensity transmitted.
Explain how polarising sunglasses reduce glare from a wet road.
Plane polarised light passes through a polariser. At what angle between the polarisation and the axis is exactly half the intensity transmitted?
Answer key and marking notes
- Its oscillations are restricted to a single plane ✓
- (perpendicular to the direction of travel) ✓
- The transmitted intensity is zero ✓
- I = I₀ cos²90° = I₀ × 0 = 0 ✓
- I = I₀ cos²45° ✓
- cos 45° = 0.707, so cos²45° = 0.50 ✓
- I = 0.50 I₀ ✓
- Fraction = cos²20° ✓
- cos 20° = 0.940, so cos²20° = 0.88 ✓
- About 0.88 (88%) is transmitted ✓
- Light reflected from the road is partially plane polarised in one direction ✓
- The sunglasses transmit only the perpendicular plane, blocking much of the reflected glare ✓
- Set cos²θ = 0.50, so cosθ = 0.707 ✓
- θ = 45° ✓
10 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Polarisation is possible only for:
- Atransverse waves
- Blongitudinal waves
- Csound waves
- Dall waves
Malus law is:
- AI = I₀ cosθ
- BI = I₀ sin²θ
- CI = I₀ cos²θ
- DI = I₀/cosθ
Polarised light meets a filter at 0° to its plane. The transmitted intensity is:
- Azero
- BI₀ (maximum)
- Chalf I₀
- Da quarter I₀
Crossed polarisers at 90° transmit an intensity of:
- AI₀
- Bhalf I₀
- Ca quarter I₀
- Dzero
Polarised light at 60° to a filter transmits a fraction:
- A0.25
- B0.50
- C0.87
- D0.75
At what angle is exactly half the intensity transmitted?
- A30°
- B60°
- C45°
- D90°
A single polariser turns unpolarised light into:
- Aunpolarised light
- Bplane polarised light
- Clongitudinal waves
- Dfaster light
That light can be polarised is evidence that light is:
- Alongitudinal
- Ba particle only
- Cslower than sound
- Dtransverse
Polarising sunglasses reduce glare by:
- Ablocking one plane of reflected polarised light
- Bslowing the light
- Cchanging the colour
- Dfocusing the light
Polarised light at 30° to a filter transmits a fraction:
- A0.50
- B0.25
- C0.75
- D0.87
Quiz key
Only transverse waves can be polarised.
I = I₀ cos²θ.
cos²0° = 1, so all the light is transmitted.
cos²90° = 0.
cos²60° = (0.5)² = 0.25.
cos²θ = 0.5 gives θ = 45°.
A polariser transmits one plane, giving plane polarised light.
Polarisation requires a transverse wave.
They block the plane in which reflected light is mostly polarised.
cos²30° = (0.866)² = 0.75.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.