DiagonixMalus’s Law / Three-Polarizer EffectSticker

Diagonix is a diplomat, and her trick is getting in the way.

Light’s electric field can oscillate in any direction across the beam. A polariser passes only the part of the oscillation along its transmission axis. Ordinary unpolarised light loses half its intensity at the first polariser and comes out vertical. Put a horizontal polariser after it and nothing gets through at all, because vertical light has no horizontal part. Two feuding border guards, one admitting only vertical travellers and one only horizontal, and nobody crosses.

Now Diagonix steps in between, tilted at 45°. The rule for light meeting a polariser at angle θ is the first line on this page, Malus’s law: the intensity drops by cos²θ. At 45° that is one half. So she lets half of the vertical travellers through, re-stamped diagonal. The horizontal guard then sees diagonal light, also 45° away, and lets half of those through. Half, then half, then half: one eighth of the original unpolarised light emerges, where before there was none. The bars on her clipboard read ½, ¼, ⅛, the last two lines.

Étienne-Louis Malus, an officer in the French corps of engineers who had served on Napoleon’s expedition to Egypt, published his discovery that reflected light is polarised in 1809. The cosine-squared rule carries his name.

The surprise is not that the middle filter adds light. It doesn’t; it only removes some. What it changes is the question the last filter gets to ask. Light that has just answered “diagonal” has a fresh, even chance of answering “horizontal”, whatever it said before.

Nothing got through. Then they added me.