1. What is Malus' Law?

Malus' Law describes how the intensity of polarized light changes as it passes through a polarizing filter. It states that the transmitted intensity I is equal to the initial intensity I₀ multiplied by the square of the cosine of the angle between the light's polarization direction and the filter's axis.

2. How Does the Calculator Work?

The calculator uses Malus' Law equation:

Where:

• \( I \) — Transmitted intensity (W/m²)
• \( I_0 \) — Initial intensity (W/m²)
• \( \theta \) — Angle between polarizer and analyzer (degrees)
• \( \phi \) — Phase angle (degrees)

Explanation: The equation shows that maximum transmission occurs when θ + φ = 0° or 180°, and minimum (zero) transmission occurs at 90° or 270°.

3. Importance of Malus' Law

Details: Malus' Law is fundamental in optics, helping design polarizing filters, LCD displays, sunglasses, and optical instruments. It's crucial for understanding light polarization phenomena.

4. Using the Calculator

Tips: Enter initial intensity in W/m², angle θ in degrees, and phase angle φ in degrees (default is 0). All values must be valid (I₀ > 0).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for I₀?
A: Sunlight is about 1000 W/m², laser pointers range from 1-5 W/m², and indoor lighting is typically 10-100 W/m².

Q2: When is the phase angle φ needed?
A: φ accounts for any initial phase difference between the polarizer and analyzer orientations. It's often 0 in basic setups.

Q3: Why is the intensity proportional to cos²θ?
A: The electric field is proportional to cosθ, and intensity is proportional to the square of the electric field.

Q4: Does Malus' Law apply to unpolarized light?
A: No, it only applies to polarized light. Unpolarized light's intensity is reduced by 50% when passing through a polarizer.

Q5: What are practical applications?
A: Used in photography filters, LCD technology, glare reduction in sunglasses, and scientific instruments measuring light polarization.