AS · Practice questions · Polarisation

Cosine squared.

Six original Cambridge-style questions on Malus law, crossed polarisers, and the wave-type test.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Malus law.

Law: I = I₀ cos²θ.
Crossed: 90° gives zero.
Test: only transverse waves polarise.

Analysis

[2 marks]

State what is meant by saying that light is plane polarised.

Its oscillations are restricted to a single plane ✓
(perpendicular to the direction of travel) ✓

Analysis

[2 marks]

Two ideal polarisers are placed with their transmission axes crossed at 90°. State the transmitted intensity and justify it with Malus law.

The transmitted intensity is zero ✓
I = I₀ cos²90° = I₀ × 0 = 0 ✓

Analysis

[3 marks]

Plane polarised light of intensity I₀ passes through a polariser whose axis is at 45° to the polarisation. Find the transmitted intensity.

I = I₀ cos²45° ✓
cos 45° = 0.707, so cos²45° = 0.50 ✓
I = 0.50 I₀ ✓

Analysis

[3 marks]

Plane polarised light meets a filter whose axis is at 20° to the light's polarisation. Find the fraction of the intensity transmitted.

Fraction = cos²20° ✓
cos 20° = 0.940, so cos²20° = 0.88 ✓
About 0.88 (88%) is transmitted ✓

Analysis

[2 marks]

Explain how polarising sunglasses reduce glare from a wet road.

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 ✓

Analysis

[3 marks]

Plane polarised light passes through a polariser. At what angle between the polarisation and the axis is exactly half the intensity transmitted?

Set cos²θ = 0.50, so cosθ = 0.707 ✓
θ = 45° ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.