What this calculator does
Malus's law works out light intensity transmitted through a polarizer at an angle to the polarization axis. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaI = I₀cos²θ; unpolarized light first halves: I = (I₀/2)cos²θ
The inputs explained
| Field | What to enter |
|---|---|
| Incident intensity (W/m²) | A number, measured in W/m². Starts at 100. |
| Angle to the transmission axis (°) | A number, measured in °. Starts at 30. |
| Incident light | Choose from Already polarized, Unpolarized. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with incident intensity
Every other input is held at the calculator’s starting values while incident intensity varies. Select any row to load that scenario into the calculator.
How the answer changes with incident intensity
| Incident intensity (W/m²) | Transmitted intensity | Fraction of incident intensity transmitted | Intensity entering this polarizer |
|---|---|---|---|
| 50 | 37.500 W/m² | 75.0% | 50.000 W/m² |
| 75 | 56.250 W/m² | 75.0% | 75.000 W/m² |
| 100 | 75.000 W/m² | 75.0% | 100.000 W/m² |
| 150 | 112.500 W/m² | 75.0% | 150.000 W/m² |
| 200 | 150.000 W/m² | 75.0% | 200.000 W/m² |
| 300 | 225.000 W/m² | 75.0% | 300.000 W/m² |