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Malus's Law Virtual Lab: Polarization and I = I₀cos²θ

Updated 2026-10-07

This Malus's law virtual lab turns the polarization practical of A-level and senior physics courses into a quick, clean data set. Light from a lamp passes through a polarizer and an analyser to a light meter. Students turn the analyser from 0° to 90°, record the reading at each angle, and plot intensity against θ and against cos²θ. The straight line through the origin confirms I = I₀cos²θ, and its gradient gives I₀. A third filter between crossed polarizers then lets light through again, which makes a good explanation question. Every number below was read from the simulation.

Polarisation and Malus's law – I = I₀cos²θ, transverse waves through slits, reflection and sunglasses
  • AQA A-level Physics 7408, section 3.3.1.2: polarization as evidence for the transverse nature of waves, with applications such as polarizing filters.
  • NSW HSC Physics, Module 7 (The Nature of Light): the investigation to verify Malus's law, I = I_max cos²θ.
  • AP Physics 2: polarization of light as a transverse electromagnetic wave.

Simulic is not affiliated with or endorsed by AQA, NESA or the College Board.

Before the lab (5 min)

Ask: "With the polarizer and analyser lined up, the meter reads I₀. You turn the analyser to 60°. What fraction of I₀ will the meter read?" Students choose ½, ¼, ⅓ or zero. On a class link this is question 1; the simulation unlocks after they answer.

Method in the simulation

  1. On the Malus's law tab, keep Source on Light (lamp), Polariser P at 0° and Room lights on unticked. Press Clear table if it has rows.
  2. Set Analyser A to 0°, wait for the meter to settle and press Record.
  3. Repeat at 15°, 30°, 45°, 60°, 75° and 90°.
  4. Switch Graph to I against cos²θ and read the best-fit line under the graph.
  5. Tick Add a middle filter, set Transmission axis M to 45° and Analyser A to 90°, and record once more.
θ (°) 0 15 30 45 60 75 90
cos²θ 1.000 0.933 0.750 0.500 0.250 0.067 0.000
I (lux)

the Malus's law tab with Source: Light (lamp), Polariser P 0° and Analyser A 60°, Graph: I against cos²θ, after recording at θ = 0°, 15°, 30°, 45°, 60°, 75° and 90° with the room lights off: the meter reading about 125 lux and the best-fit line under the graph about I = 500·cos²θ

Expected results

The meter adds a fluctuation of about ±0.4 %, so readings differ slightly between groups.

  • One browser run: 500.1, 463.2, 373.4, 251.1, 125.6, 33.3 and 0.0 lux for θ = 0° to 90°. Four more readings at 60° gave 124.6–125.0 lux.
  • Graph: I against θ is an S-shaped curve; I against cos²θ is a straight line through the origin. Three runs gave best-fit lines with gradients of 498.2, 499.8 and 499.3 lux and intercepts within 0.1 lux of zero.
  • Why I₀ = 500 lux: the lamp gives 1000 lux, and the first polarizer passes half of unpolarized light.
  • Middle filter at 45° between crossed filters: 125.3 lux, a quarter of I₀.
  • Room lights on at 90°: 7.9 lux of background instead of zero. With that point included, the gradient dropped to 496.1 lux.

Questions for students

  1. (Prediction, asked again after the lab) At θ = 60°, what fraction of I₀ does the meter read?
  2. Which quantities must stay the same while you turn the analyser?
  3. With P = 0° and A = 60°, what does the meter read?
  4. What is the gradient of your graph of I against cos²θ?
  5. Explain why a middle filter at 45° lets light through two crossed polarizers.

Answers for teachers: (1) ¼, because cos²60° = 0.25. (2) The lamp, the polarizer angle P and the room lights (off). (3) Accept 122–128 lux. (4) Accept 495–505 lux; it equals I₀. (5) Each filter passes the component of the electric field along its axis. Light leaving P has its field at 0°; the middle filter passes cos²45° = ½ of it, now polarized at 45°; the analyser at 90° is 45° from that and passes another half. I = 500 × ½ × ½ = 125 lux.

Common misconceptions

  • "The intensity falls in proportion to the angle." At 30° the meter reads 373 lux, not two thirds of 500. Intensity depends on cos²θ.
  • "Adding a filter can only block more light." The middle filter turns 0 lux into 125 lux.
  • "Any wave can be polarized." Only transverse waves: the Waves at slits tab shows a longitudinal wave on a spring passing a slit at any angle.

Extension

  • Microwaves: set Source to Microwaves and repeat. The transmitter is already polarized, so I₀ is 100 on the meter's scale; a metal grille plays the part of the middle filter.
  • Glare: on Reflection and sunglasses, press Go to Brewster angle for water (about 53°) and compare the glare with and without Polarising sunglasses.

FAQ

Can I pin the angles for my class?

Yes. On the Share page, pin Polariser (or transmitter) axis P, Analyser (or receiver) axis A and Room lights on in the link's starting values. The class link opens on the Malus's law tab.

Why does the reading flicker?

The model adds a small random fluctuation, like a real light meter. Wait a moment before pressing Record, or record twice and take the mean.

Why is the reading not zero at 90° with the room lights on?

Room light reaches the meter without passing through the filters. Read this background at θ = 90° and subtract it from every reading before plotting.

Electromagnetic spectrum explorer – wavelength, frequency, photon energy, sources, uses and dangers Transverse and longitudinal waves – how the particles move

For more on light, see the refraction and lenses lesson plan and interactive physics lesson ideas.

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