The Memory Trick
💡 Half Gone Immediately, Then Malus's Law
Unpolarized light has its electric field oscillating in every possible transverse direction simultaneously. Passing it through a single linear polarizer immediately cuts its intensity exactly in half (I = I₀/2), since the polarizer only passes the one component of oscillation aligned with its own axis. Passing that now-polarized light through a SECOND polarizer (an 'analyzer') set at an angle θ to the first follows Malus's Law: I = I₀cos²θ.
Why It Works
At θ=0° (analyzer aligned with the first polarizer), cos²0°=1, so all the already-polarized light passes through unchanged. At θ=90° (crossed polarizers), cos²90°=0, so absolutely NO light passes through at all — this predictable, calculable blocking behavior is exactly what makes polarizing filters so useful across photography, LCD screens, and 3D movie technology.
Step by Step
Applications of Polarization
1
Brewster's angle — naturally polarized reflection
At one specific angle of incidence (Brewster's angle, where tan θB = n₂/n₁), reflected light becomes completely, perfectly polarized — this is the physical basis for why polarized sunglasses are so effective at cutting glare specifically from horizontal surfaces like water and roads.
Reflected glare off a lake surface is largely polarized due to this Brewster's angle effect, which is exactly why polarized sunglasses (oriented to block that specific polarization) cut glare so effectively.
2
LCD screens rely on controllable polarization
LCD (liquid crystal display) screens use two polarizing filters with liquid crystal material between them — applying an electric voltage to the liquid crystal rotates the polarization of passing light by a controllable amount, precisely controlling how much light gets through the second polarizer at each pixel.
This voltage-controlled polarization rotation is the fundamental mechanism behind every LCD screen's ability to display different brightness levels at each pixel.
3
3D movies use polarization to send different images to each eye
Many 3D movie systems project two slightly different images using two different polarization orientations simultaneously, with the viewer's 3D glasses containing two differently-oriented polarizing lenses — each eye's lens blocks the image intended for the OTHER eye, letting each eye see only its own designated image.
This is why 3D glasses appear to have identical-looking lenses at a glance, but are actually oriented at different polarization angles for the left versus right eye.
🏥 Worked Example
Unpolarized light of intensity 100 W/m² passes through a polarizer, then through a second polarizer (analyzer) oriented at 30° to the first. What is the final intensity?
1
First polarizer — unpolarized light loses half its intensity: I₁ = 100/2 = 50 W/m².
2
Second polarizer (analyzer) — apply Malus's Law: I₂ = I₁cos²(30°).
3
Solve: cos(30°) ≈ 0.866, so cos²(30°) ≈ 0.75; I₂ = 50 × 0.75 = 37.5 W/m² — the final intensity after passing through both polarizers.
📌 Exam Application
Exams test correctly applying the initial halving rule for unpolarized light through a first polarizer, then correctly applying Malus's Law for a second polarizer at a given angle, and understanding Brewster's angle and practical polarization applications.
⚠️ Most Common Polarization of Light Mistakes
The most common trap is applying Malus's Law directly to UNPOLARIZED light hitting the first polarizer — Malus's Law (I=I₀cos²θ) only applies to already-polarized light passing through a SECOND polarizer at some angle; the first polarizer always simply halves unpolarized light's intensity, regardless of its own orientation.
✓ Quick Self-Test
1) What happens to unpolarized light's intensity when it passes through a single linear polarizer? It's cut exactly in half (I = I₀/2). 2) Write Malus's Law. I = I₀cos²θ, where θ is the angle between the polarizer and analyzer. 3) What happens to light intensity when passing through two 'crossed' polarizers (oriented 90° apart)? Zero light passes through (I=0). 4) What is Brewster's angle, and why does it matter for sunglasses? The angle of incidence at which reflected light becomes completely polarized; it's why polarized sunglasses are especially effective at reducing glare from water and roads. 5) How do 3D movie glasses use polarization to show different images to each eye? Each lens is oriented at a different polarization angle, blocking the image intended for the OTHER eye and letting each eye see only its own designated image.