Crossed polars + middle filter paradox
● VERBATIM — examined word-for-wordCrossed pair alone: zero. Insert a middle polaroid at 45°: I = I₁cos²45° × cos²45° = I₁/4 ≠ 0 — the middle filter rotates the polarisation plane, reopening the door. Minimum transmission through a chain ⇔ some consecutive pair perpendicular; give BOTH angle answers in 0–360° (e.g. 120° and 300°).
What this actually means
Crossed polarisers alone pass nothing: cos²90° = 0. Slide a third polaroid at 45° BETWEEN them and light gets through again, a quarter of the polarised input.
The middle filter works by rotating the polarisation plane in two 45° steps, so no single step ever meets a 90° gap. Adding a filter added light, which is the paradox examiners love.
For minimum transmission through any chain, hunt for a consecutive pair at right angles, and give both solutions in 0 to 360°, for example 120° and 300°.
Prove it — watch it be true
- Load the crossed + middle-filter preset: crossed pair alone reads zero
- Insert the 45° middle filter: the output meter jumps to I₁/4
- Rotate the middle filter to 0° or 90°: back to darkness — the rotation was doing the work