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.
Turn the second polarizer's angle and watch the transmitted beam dim exactly following Malus's law. Turn on the middle polarizer to see light reappear through two "crossed" filters.
About the Polarization of Light: Malus's Law Lab
Free 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. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the polarization of light: malus's law lab runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
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. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use 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.
- Press "Source intensity I₀ = 100%", "Reset to defaults", "Lab Report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- 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.
- Predict the final brightness before checking the readout.
Key ideas you can learn
- 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.
- Polarizing sunglasses and camera filters use Malus's law to cut glare, which is itself partially polarized by reflection.
Show my work
Challenges
Challenge 1 - dim it to 25%
Turn off the middle polarizer. Set the angle θ between P1 and P2 so the light coming out of P2 is 25% of I₁ (the intensity right after P1). Use I₂ = I₁ cos²θ. Enter the angle in degrees you used.
Challenge 2 - reviving crossed polarizers
Set θ = 90° (P1 and P2 crossed, no light gets through). Now turn on the middle polarizer P3 at 45° from P1. What fraction of I₁ now makes it through all three filters? Compute I_middle = I₁cos²(45°), then I_final = I_middle × cos²(90°-45°), and enter the final fraction as a percentage of I₁.
Where this is used in the real world
LCD screens, polarized sunglasses, camera polarizing filters and stress analysis in engineering plastics all rely directly on Malus's law and controlled polarization.
Who is this simulation for?
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. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
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. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Polarization of Light: Malus's Law Lab work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.