This simulator sends unpolarized light through a fixed first polarizer, then through a second polarizer (the analyzer) at an angle you control, tracking exactly how much light gets through at every angle according to Malus's law.
• A full optical path: an unpolarized source, a fixed polarizer, a rotatable analyzer disk, and a brightness detector with a live bar-graph readout. • One live control: analyzer angle (0°-180°), plus an animate button that sweeps it continuously. • Live readouts for the analyzer angle, cos²θ, and the transmitted intensity as a percentage of the incoming polarized light. • Four preset angles: aligned (0°), 45°, crossed (90°), and 135°.
Once light is linearly polarized by the first filter, passing it through a second polarizer set at angle θ to the first transmits intensity I = I₀cos²θ, where I₀ is the intensity after the first polarizer. At θ = 0° (aligned), all of that light passes (cos²0° = 1). At θ = 90° (crossed polarizers), none of it passes (cos²90° = 0) — the classic demonstration used to explain polarized sunglasses and LCD screens.
Unpolarized light contains equal amounts of every polarization orientation. A single ideal polarizer transmits, on average, exactly half the incoming intensity regardless of its own orientation — this is sometimes called the "unpolarized-to-polarized" 50% rule, distinct from Malus's law, which only applies to light that is already polarized passing through a second filter.
I = I₀cos²θ, where I₀ is the intensity of light already polarized by a first filter, θ is the angle between that filter and a second polarizer (the analyzer), and I is the intensity transmitted through the second filter.
At θ = 90°, cos²θ = 0, so Malus's law predicts zero transmitted intensity — the analyzer's transmission axis is perpendicular to the light's polarization direction, blocking it completely.
On average, exactly half the incoming intensity, regardless of the polarizer's orientation — this is a separate rule from Malus's law, which governs a second polarizer acting on already-polarized light.
Polarizing sunglasses block horizontally polarized glare, LCD screens use crossed polarizers with a liquid-crystal layer between them to control pixel brightness, and polarizing filters on cameras reduce reflections and boost sky contrast.