Polarization of Light (Malus's Law)
Malus's Law I = I₀cos²θ with two-polarizer system. Adjust polarizer angles and see transmitted intensity change. Crossed polarizers block all light.
WHAT IS POLARIZATION?
Polarization is a property of transverse waves, like light, that describes the orientation of their oscillations. For an electromagnetic wave, the **direction of polarization** is defined as the plane in which the electric field oscillates. Most natural light (like sunlight) is unpolarized, meaning it contains waves oscillating in all possible directions perpendicular to travel.
POLARIZING FILTERS
A polarizer is a material that allows only light waves with a specific electric field orientation to pass through. When unpolarized light hits a polarizer, its intensity is cut in half. If light that is already polarized hits a second filter (an analyzer), the amount of light that passes through depends on the angle between the two filters, following **Malus's Law**.
HOW TO USE THIS VISUALIZATION
1. **Rotate the Filter**: Spin the first polarizer and watch how it selects an orientation. 2. **Add an Analyzer**: Place a second filter. Rotate it to 90° (crossed polarizers) and watch the light disappear entirely. 3. **Insert a Third Filter**: Place a filter at 45° between the two crossed polarizers. Observe the surprising result: light reappears!
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 6: Geometric and Physical Optics (Topic 6.4)
Learning Objective: OPT-1.A
COMMON MISCONCEPTIONS
- Thinking longitudinal waves (like sound) can be polarized.
- Believing a polarizer works like a "sieve" for particles.
- Forgetting that intensity depends on the SQUARE of the cosine.
KEY TAKEAWAYS
- Only transverse waves can be polarized.
- Malus's Law governs intensity through multiple filters.
- Crossed polarizers block all light.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): Polarized light of intensity hits a filter at 60° to its axis. What is the transmitted intensity?
Show Answer & Explanation
Answer: 0.25 I_0
Explanation: .
Q2 (CONCEPTUAL): Why does light disappear when two polarizers are at 90° to each other?
Show Answer & Explanation
Answer: The second filter blocks all oscillations passed by the first.
Explanation: The first filter polarizes light vertically (for example). The second filter only passes horizontal light. Since there is no horizontal component in vertically polarized light, nothing passes.
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