What does Malus's Law assume?

It assumes perfectly polarized incident light and an ideal polarizer with no absorption losses. Real polarizers have some residual transmission even at 90°.

What happens with unpolarized light?

The first polarizer transmits exactly half the unpolarized light. After that, Malus's Law applies to subsequent polarizers.

What is the extinction ratio?

The ratio of maximum to minimum transmission, usually expressed in dB. A good polarizer has an extinction ratio > 30 dB.

How do LCD screens use this?

LCDs use two crossed polarizers with a liquid crystal layer between them. The LC rotates light polarization to control transmission per pixel.

Can multiple polarizers transmit through 90°?

Yes! N polarizers each stepped by 90°/(N−1) transmit more than two crossed ones. As N → ∞, transmission approaches I₀ (QZE analog).

Does wavelength affect the result?

Ideal Malus's Law is wavelength-independent, but real polarizers may have wavelength-dependent extinction ratios.

Malus's Law Calculator

Calculate the intensity of polarized light after passing through an analyzer at any angle using Malus's law, with multi-polarizer chain analysis.

Incident Intensity (I₀)

Polarizer Angle (θ)

Angle Unit

Multi-Polarizer Chain

Number of Polarizers

Total Rotation (°)

Transmitted Intensity

50.0000

I = I₀ × cos²(θ) — Malus's Law

Transmission

50.00%

Fraction of light passing through

Extinction

50.00%

Fraction of light blocked

Extinction Ratio

3.01 dB

−10 × log₁₀(T) — higher means more blocking

Angle

45.00°

Angle between polarizer axes

Multi-Polarizer Output

0.0000

2 polarizers spanning 90° total

Transmission vs Angle

0°

10°

20°

30°

45°

60°

70°

80°

90°

Angle (°)	cos²θ	Intensity
0°	1.0000	100.00
10°	0.9698	96.98
20°	0.8830	88.30
30°	0.7500	75.00
45°	0.5000	50.00
60°	0.2500	25.00
70°	0.1170	11.70
80°	0.0302	3.02
90°	0.0000	0.00

Planning notes, formulas, and examples

About the Malus's Law Calculator

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.

When This Page Helps

This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows.

How to Use the Inputs

Enter the incident intensity of the polarized light entering the analyzer.
Enter the angle between the polarizer and analyzer axes.
Select degrees or radians for the angle unit.
For multi-polarizer analysis, enter the number of polarizers and total rotation.
Review the transmitted intensity, transmission, extinction ratio, and multi-polarizer output.
Study the angle-intensity table and visual chart.

Formula used

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)

Example Calculation

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.

Tips & Best Practices

Check that all inputs use the same scale and assumptions before trusting the result.
Compare the answer with the worked example or a rough estimate to catch entry mistakes.

When To Use This Calculator

Calculate the intensity of polarized light after passing through an analyzer at any angle using Malus's law, with multi-polarizer chain analysis. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

It assumes perfectly polarized incident light and an ideal polarizer with no absorption losses. Real polarizers have some residual transmission even at 90°.