Explore Malus's Law, linear & circular polarization, and the effects of birefringent wave plates.
Final Intensity
100%
θ = 0°
Malus's Law
I = I₀ × cos²(θ)
Current angle θ and intensity ratio shown above.
About This Graph
Shows how transmitted intensity varies with the angle between two polarizers. The graph shows I = I₀·cos²(θ), where θ is the angle between the polarization axis of the first polarizer and the transmission axis of the analyzer. The red dot indicates your current analyzer angle setting.
Pol 1:
0°
Analyzer:
90°
I₀
100%
After Pol 1
50%
After Analyzer
0%
Classic Problem
Experiment: Try 0° → 45° → 90°. Light gets through! But 0° → 90° blocks it all.
Why? Each 45° step only reduces by cos²(45°) ≈ 0.5. Total: 0.5 × 0.5 = 0.25 (25%). But direct 90° gives cos²(90°) = 0.
Malus's Law
When polarized light passes through a polarizer, the transmitted intensity is:
I = I₀ × cos²(θ)
where θ is the angle between the incident polarization and the transmission axis.
Polarization States
Linear: E oscillates in one plane.
Circular: E rotates in a circle (phase difference λ/4).
Elliptical: E traces an ellipse (arbitrary phase).
Wave Plates
λ/4 Plate: Introduces π/2 phase difference. Converts linear → circular.
λ/2 Plate: Introduces π phase difference. Rotates linear polarization.