Malus Law Calculator
Calculate the intensity of polarized light transmitted through a polarizer
Intensity of polarized light before the analyzer
Angle between polarization directions of polarizer and analyzer
How to Use This Calculator
Enter Initial Intensity
Input the intensity of the polarized light before it passes through the analyzer polarizer. This can be in any units (watts, arbitrary units, etc.).
Enter the Angle
Input the angle between the polarization direction of the initial polarizer and the analyzer polarizer in degrees. At 0°, maximum transmission occurs; at 90°, minimum (zero) transmission occurs.
Calculate
Click the "Calculate Transmitted Intensity" button to get the intensity of light that passes through the analyzer, as well as the percentage of initial intensity.
Formula
I = I₀ × cos²(θ)
Where:
- I = Transmitted intensity (in same units as I₀)
- I₀ = Initial intensity of polarized light
- θ = Angle between polarization directions (in degrees or radians)
Example Calculation:
For initial intensity of 100 units at 45° angle:
I₀ = 100
θ = 45°
I = 100 × cos²(45°)
I = 100 × (0.707)²
I = 100 × 0.5 = 50
At 45°, exactly half the intensity is transmitted.
Special Angles:
• At 0°: I = I₀ (maximum transmission, 100%)
• At 45°: I = I₀/2 (50% transmission)
• At 90°: I = 0 (no transmission, complete blocking)
About Malus Law Calculator
Malus's law describes how the intensity of polarized light changes when it passes through a polarizing filter (analyzer) that is rotated relative to the initial polarization direction. The law states that the transmitted intensity is proportional to the square of the cosine of the angle between the polarization directions. This is fundamental to understanding polarized light, optical filters, and many optical devices.
When to Use This Calculator
- Optical Experiments: Calculate expected transmission through polarizers in experiments
- Optical Design: Design systems using polarizers and understand light transmission
- Photography: Understand how polarizing filters affect light intensity
- Research: Analyze polarized light interactions and optical systems
- Educational Purposes: Learn about polarization and Malus's law
Why Use Our Calculator?
- ✅ Instant Results: Get accurate intensity calculations immediately
- ✅ Easy to Use: Simple interface requiring only intensity and angle
- ✅ Percentage Display: Shows both absolute intensity and percentage
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
Common Applications
Photography: Photographers use polarizing filters to reduce reflections and enhance colors. Understanding Malus's law helps predict how much light will be blocked at different filter angles, affecting exposure settings.
Optical Instruments: Many optical instruments use polarizers for analysis, modulation, or filtering. Malus's law helps design these systems and predict performance.
LCD Displays: Liquid crystal displays use polarizers to control light transmission. Understanding Malus's law is essential for LCD design and optimization.
Tips for Best Results
- Angle is measured between the polarization directions of the two polarizers
- At 0°, polarizers are aligned and maximum light passes through
- At 90°, polarizers are crossed and no light passes through
- The intensity follows a cos² dependence, so it drops quickly from 0°
- At 45°, exactly half the intensity is transmitted (cos²(45°) = 0.5)
- Remember that initial light must be polarized for Malus's law to apply
Frequently Asked Questions
What is Malus's law?
Malus's law states that the intensity of polarized light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization directions. It's named after Étienne-Louis Malus, who discovered it in 1809.
Why is it cos²(θ) and not just cos(θ)?
The cos² dependence comes from the fact that the electric field component parallel to the analyzer's transmission axis is proportional to cos(θ), and intensity is proportional to the square of the electric field. Therefore, I ∝ E² ∝ cos²(θ).
Does this work for unpolarized light?
Malus's law applies specifically to polarized light. For unpolarized light passing through a polarizer, the transmitted intensity is always I₀/2, regardless of the polarizer's orientation (after the first polarizer creates polarized light).
What happens at 45 degrees?
At 45°, cos(45°) = √2/2 ≈ 0.707, so cos²(45°) = 0.5. This means exactly half the intensity is transmitted. This is a convenient reference point for experiments and calculations.
Can I use this for multiple polarizers?
For multiple polarizers in sequence, apply Malus's law step by step. The output intensity from one polarizer becomes the input intensity for the next. Each polarizer reduces the intensity according to the angle between it and the previous polarizer.