Optics
Crossed polarizers
Two polarizers at 90° block all light (Malus: I = I₀cos²θ → 0).
Crossed polarizers — interactive Optics simulation. Two polarizers at 90° block all light (Malus: I = I₀cos²θ → 0). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Malus law
Two polarizers at 90° block all light (Malus: I = I₀cos²θ → 0).
Polarizers transmit only the component of electric field along their axis. At 90° cross, no component survives. Malus's law predicts intensity I = I₀ cos²θ between angles—foundation for polarized sunglasses and LCD displays.
- I = I₀ cos²θ
- Crossed → dark
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Light passes through one polarizer, then a second one at some angle to the first. Does the transmitted intensity depend smoothly on the angle between the two polarizers' axes?
Predictions to weigh
- Transmitted intensity decreases linearly with the angle.
- Light either passes completely or is completely blocked — no smooth transition.
- Yes — transmitted intensity follows cos² of the angle between the axes, reaching zero at exactly 90° ('crossed' polarizers).
Variable roles
What you set:
- Angle between axes Δθ (°)
What you measure:
- Transmitted fraction (through P2)
How the investigation runs
- Open the crossed-polarizers preset and press Reset. The two polarizers' axes are set 90° apart (fully crossed — no light transmitted).
- Enable the transmitted-intensity readout.
- Set the angle between the two polarizers' axes for each trial and record the fraction of light transmitted through the second one.
Governing equation
Malus's Law — I = I₀·cos²θ
Light already polarized along one axis, passing through a second polarizer at angle Δθ to the first, transmits a fraction cos²(Δθ) of its intensity. At Δθ = 90° ('crossed'), transmission drops to exactly zero.
What the printable worksheet asks students to work out
- For one trial, compute the fraction transmitted through the second polarizer as 0.5·cos²(Δθ) — the 0.5 is the unpolarised source losing half its intensity at the first polarizer, and cos²(Δθ) is Malus's law at the second. Compare to the table.
- Explain why the fraction transmitted through P2 depends only on the ANGLE BETWEEN the two axes, not on their absolute orientation — and why exactly 90° ('crossed') gives zero transmission.
Where this shows up beyond the lab
- Polarized sunglasses block horizontally-polarized glare (like reflections off water or roads) by orienting their polarizing axis vertically. Explain, using Malus's law, why tilting your head sideways while wearing polarized sunglasses can make glare suddenly reappear.
- LCD screens use crossed polarizers with a liquid crystal layer between them that can rotate light's polarization on command, controlling how much light gets through each pixel. Explain why 'crossed' (rather than parallel) polarizers are the natural default 'off' state for a pixel.
- AP Physics 2 — Unit 14: Waves, Sound, and Physical Optics
- IB Physics — C.3 Wave phenomena
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Crossed Polarizers
- Select the first polarizer
- Press Play
- Intensity through polarizers
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.