Malus Law Calculator

Malus's law gives how much polarized light passes through a polarizer at an angle.

How the Math Works

Malus's Law describes how the intensity of polarized light changes when passing through a polarizing filter. The formula I = I₀·cos²θ calculates the transmitted intensity (I) based on the initial intensity (I₀) and the angle (θ) between the light's polarization direction and the polarizer's axis. The cosine squared term arises because the polarizer only allows the component of the electric field aligned with its axis to pass through. Squaring this component accounts for the proportional relationship between electric field amplitude and light intensity. When θ is 0°, the full intensity passes (I = I₀), but at 90°, the intensity drops to zero (cos²90° = 0), demonstrating complete blockage.

Practical Applications

This calculation is essential in optics experiments and engineering design. For example, in physics labs, students use Malus's Law to verify the relationship between light intensity and polarizer angles. Optical engineers apply it when designing devices like LCD screens, where liquid crystals rotate polarization to control pixel brightness. Camera photographers use polarizing filters to reduce reflections and enhance contrast by calculating the optimal filter rotation angle. Additionally, it's critical in designing safety equipment like polarized sunglasses, ensuring they block specific glare angles while maintaining visibility.

Day-to-Day Use

You encounter Malus's Law in everyday items like polarized sunglasses, which cut glare from roads or water by blocking horizontally polarized light. Camera polarizers rely on this principle to reduce reflections in photos of windows or water surfaces. Even LCD screens on phones and computers use controlled polarization to create images, as liquid crystals adjust their orientation to modulate light. These applications improve visual comfort, enhance photography, and enable modern display technology, making the invisible mechanics of light interaction with materials a tangible part of daily life.

Worked example

100 W/m² at 30° → 75 W/m².

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