Explore the Polarization of Light: Malus's Law Lab
Turn a polarizing filter and watch the transmitted light dim exactly as I = I0 cos²θ predicts. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Polarization of Light: Malus's Law Lab with sample data entered and the result showing.
What is the Polarization of Light: Malus's Law Lab?
Turn a polarizing filter and watch the transmitted light dim exactly as I = I0 cos²θ predicts, then bring light back through crossed filters with a third one. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
LCD screens, polarized sunglasses, camera polarizing filters and stress analysis in engineering plastics all rely directly on Malus's law and controlled polarization.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Malus's law: light transmitted through a polarizer is I = I0 cos²θ, where θ is the angle between the light's polarization and the filter's axis.
Unpolarized light loses exactly half its intensity passing through the first polarizer, regardless of that polarizer's angle.
Two polarizers at 90° to each other (crossed) block all light - but inserting a third polarizer at an angle between them lets some light back through.
Rotate the second polarizer through 90° and watch the beam fade to black.
Turn on the middle polarizer at 45° between two crossed filters and see the light return.
Try the 25%-transmission angle challenge.
Used for
Pick one to see how it fits.
Physics learners
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams.
Try it freeTeachers
For teachers: project the Polarization of Light: Malus's Law Lab on the board, let students predict the result, then run it together and test this: Turn on the middle polarizer at 45° between two crossed filters and see the light return. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
Why does inserting a middle polarizer between two crossed polarizers let light through again?
Each polarizer only projects the light onto its own axis; the middle filter re-polarizes the light along a new direction that is no longer exactly perpendicular to the final filter, so some component gets through both remaining stages.
Why does unpolarized light lose exactly 50% of its intensity through the first polarizer?
Unpolarized light has its electric field oriented in all directions with equal probability, and averaging cos²θ over all those angles gives exactly 1/2.
Is the Polarization of Light: Malus's Law Lab free to use?
Yes. The Polarization of Light: Malus's Law Lab is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.
Does the Polarization of Light: Malus's Law Lab work on a phone or tablet?
Yes. The Polarization of Light: Malus's Law Lab takes touch input as well as mouse input, so you can use its 3 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Polarization of Light: Malus's Law Lab?
1. In the Polarization of Light: Malus's Law Lab, use the controls to change Angle between P1 and P2 (θ), Insert middle polarizer P3, P3 angle (measured from P1). The simulation reacts instantly. 2. In the Polarization of Light: Malus's Law Lab, press "Source intensity I₀ = 100%" to start, reset or change what is happening. 3. Start with this experiment: Rotate the second polarizer through 90° and watch the beam fade to black. Drag any glowing handle, object or slider with your mouse or finger and the Polarization of Light: Malus's Law Lab responds in real time. 4. Change one setting at a time and watch which readout moves, then compare it with this idea: Malus's law: light transmitted through a polarizer is I = I0 cos²θ, where θ is the angle between the light's polarization and the filter's axis.
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Try the Polarization of Light: Malus's Law Lab now
Turn a polarizing filter and watch the transmitted light dim exactly as I = I0 cos²θ. Free to use.
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