Calculate the intensity of polarized light after passing through an analyzer at any angle using Malus's law, with multi-polarizer chain analysis.
Malus's Law describes how the intensity of polarized light changes when it passes through a polarizing filter. The transmitted intensity follows a simple cos²θ relationship, where θ is the angle between the polarization direction and the filter's transmission axis. At 0° the light passes fully; at 90° (crossed polarizers) it is completely blocked.
This principle underlies LCD displays, polarizing sunglasses, glare reduction in photography, stress analysis in photoelasticity, and optical instruments. It is also key to understanding quantum measurement in polarization-based quantum optics experiments.
This calculator computes the transmitted intensity, transmission percentage, extinction ratio in dB, and handles multi-polarizer chains where multiple polarizers are stacked at evenly spaced angles. Preset buttons cover common scenarios from crossed polarizers to LCD subpixels. A visual bar chart and complete angle-intensity table provide comprehensive reference. The multi-polarizer feature demonstrates the fascinating result that many small rotations can transmit more light than a single large rotation.
This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows. This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Malus's Law: I = I₀ × cos²(θ) Extinction Ratio: ER = −10 × log₁₀(I/I₀) dB Multi-polarizer: I = I₀ × [cos²(Δθ)]^(N−1), where Δθ = total_angle / (N−1) At θ = 45°: I = I₀/2 (half intensity) At θ = 90°: I = 0 (complete extinction)
Result: I = 50, Transmission = 50%, ER = 3.01 dB
At 45° between polarizer axes, exactly half the polarized light intensity is transmitted — a result that follows directly from cos²(45°) = 0.5.
Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.
Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.
Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.
It assumes perfectly polarized incident light and an ideal polarizer with no absorption losses. Real polarizers have some residual transmission even at 90°.
The first polarizer transmits exactly half the unpolarized light. After that, Malus's Law applies to subsequent polarizers.
The ratio of maximum to minimum transmission, usually expressed in dB. A good polarizer has an extinction ratio > 30 dB.
LCDs use two crossed polarizers with a liquid crystal layer between them. The LC rotates light polarization to control transmission per pixel.
Yes! N polarizers each stepped by 90°/(N−1) transmit more than two crossed ones. As N → ∞, transmission approaches I₀ (QZE analog).
Ideal Malus's Law is wavelength-independent, but real polarizers may have wavelength-dependent extinction ratios. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.