Malus Law Calculator

Malus law describes how a polarizer reduces light intensity based on the angle between the polarization direction and the polarizer axis. At 90°, all light is blocked.

🔍 Optics📐 I = I₀cos²θ🎨 Polarization

Initial Intensity I₀ (W/m²)

Angle θ (deg)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Transmitted Intensity	I	I = I₀cos²θ	W/m²
Initial Intensity	I₀	I₀ = I/cos²θ	W/m²
Angle	θ	Between polarization and polarizer axis	deg
Transmission	T	T = cos²θ = I/I₀	—

Step-by-Step Examples

Example 1

Crossed Polarizers

Two polarizers at 90°.

I = I0 * cos^2(90) = I0 * 0 = 0
All light blocked

✓ Zero transmission at 90°

Example 2

45 Degree

I0 = 200 W/m^2, theta = 45°.

I = 200 * cos^2(45) = 200 * 0.5
I = 100 W/m^2

✓ 50% transmitted at 45°

Example 3

30 Degree

I0 = 100 W/m^2, theta = 30°.

I = 100 * cos^2(30) = 100 * 0.75 = 75 W/m^2

✓ 75% transmitted at 30°

Real-World Applications

🕶️

Sunglasses

Polarized sunglasses block reflected glare (which is polarized horizontally).

📷

Photography

Polarizing filters reduce reflections from water and glass in photos.

💻

LCD Displays

LCD screens use two polarizers with liquid crystal rotating polarization to control pixel brightness.

🔬

Stress Analysis

Photoelastic stress analysis uses polarized light to visualize stress in transparent materials.

Common Mistakes to Avoid

⚠️

Applying to unpolarized light

Unpolarized light through first polarizer: I = I0/2 (regardless of angle). Malus law applies to already-polarized light.

⚠️

Forgetting squared cosine

I = I0*cos^2(theta), not I0*cos(theta). The squaring means intensity drops faster than amplitude.

⚠️

Convention for angle

Theta is between the incoming polarization direction and the transmission axis of the polarizer.

Frequently Asked Questions

Why cos squared not just cos? ▾

Amplitude of electric field goes as cos(theta). Intensity is proportional to amplitude squared, giving cos^2(theta).

What does a polarizer do? ▾

Passes only the component of electric field parallel to its transmission axis. Blocks the perpendicular component.

What is a wave plate? ▾

Introduces a phase difference between polarization components without reducing intensity. Quarter-wave plates convert linear to circular polarization.

How do LCD screens use polarization? ▾

LCD pixel = two perpendicular polarizers with liquid crystal between. Crystal rotates polarization to let light through (on) or not (off).

What is circular polarization? ▾

When two equal-amplitude perpendicular components are 90 degrees out of phase. Does not follow Malus law the same way as linear polarization.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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