Polarized light of intensity 80 W/m² hits a polarizer whose transmission axis is 60° from the light's polarization direction. What is the transmitted intensity?
A40 W/m²
B20 W/m²
C69 W/m²
D0 W/m²
I = I₀ cos²θ = 80 · cos²60° = 80 · (0.5)² = 80 · 0.25 = 20 W/m². The common mistake is using cosθ: 80 · cos60° = 40 W/m². Intensity is proportional to E², not E, so the cosine must be squared.
Question 2 Short Answer
Unpolarized light passes through two polarizers. The first is oriented vertically. The second is oriented 30° from vertical. What fraction of the original intensity exits the second polarizer?
Think about your answer, then reveal below.
Model answer: The first polarizer transmits I₀/2 (unpolarized → first polarizer always halves intensity, regardless of orientation). The second polarizer transmits I₀/2 · cos²30° = I₀/2 · 0.75 = 3I₀/8. So the final intensity is 3/8 = 37.5% of the original.
Apply the two-step process: (1) unpolarized to first polarizer always gives I₀/2; (2) first-polarized light to second polarizer gives Malus's Law with the angle between the two transmission axes. Never apply Malus's Law to the first polarizer acting on unpolarized light.
Question 3 Short Answer
Why does inserting a polarizer at 45° between two crossed (90°-apart) polarizers allow some light through, when the two crossed polarizers alone transmit no light?
Think about your answer, then reveal below.
Model answer: The two crossed polarizers alone: light polarized by the first hits the second at 90°, giving cos²90° = 0. With a middle polarizer at 45°: light polarized by the first passes through the middle at angle 45° with intensity I₀/2 · cos²45° = I₀/4, now polarized at 45°. This light hits the final polarizer at 45° from its axis: I₀/4 · cos²45° = I₀/8. Non-zero light emerges because each step rotates the polarization axis — the middle polarizer changes the polarization state, not just the intensity.
This result demonstrates that polarizers are not simply passive blockers — they actively change the polarization direction of transmitted light. The middle polarizer 'rotates' the polarization axis in stages, allowing the final crossed polarizer to receive some component.