Malus' Law and Multiple Polarizers
Malus' law states that linearly polarized light of intensity I_in incident on an ideal analyser whose axis is at angle theta to the polarization emerges with intensity I_out = I_in cos^2(theta). Apply it sequentially through multiple sheets.
Why this shows up in the exam
Variable optical attenuators · Polarization experiments · Display optics
Learn the idea
Each analyser transmits the squared cosine of the angle from the incoming linear polarization. A polarizer is a directional gate. A tilted gate passes only a projection; because intensity follows field squared, the factor is cos squared.
🧠 Memory hook: Project, square, then repeat.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I_out = I_in cos²(theta) — Malus' law
- I_N = (I_unpolarized/2) product cos²(theta_k) — sequential ideal polarizers
How to approach it
- 1Track the polarization axis after each sheet
- 2Use the angle between consecutive axes
- 3Multiply every transmission factor
Common slip-ups that cost marks
- •Using the angle to the original axis at every sheet
- •Forgetting the first one-half for unpolarized light
- •Assuming crossed outer polarizers always block when an intermediate sheet is present
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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