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Unpolarised → polariser: HALF

● VERBATIM — examined word-for-word

Unpolarised light = random mix of all oscillation planes. An ideal polariser transmits exactly ½ the intensity, regardless of orientation (average of cos²θ = ½), output polarised along its axis. This ½ comes before any Malus step — forgetting it is THE classic error (I₀/8, not I₀/4).

I after first polariser = I₀/2

What this actually means

Unpolarised light is a rapidly changing random mix of every oscillation direction. A polariser passes the component along its axis, and averaging cos²θ over all random angles gives exactly one half.

So the first polariser transmits I₀/2 whatever its orientation, and the light leaves polarised along that polariser's axis.

This half comes BEFORE any Malus calculation. The classic error chain: forget the half and get I₀/4 where the answer is I₀/8.

The trap

Forgetting the ½ step for unpolarised light before applying Malus' law.

Prove it — watch it be true

  1. Switch to unpolarised light and watch the first meter
  2. Rotate the polariser anywhere you like: the meter is parked at 50%
  3. That flat 50% is the averaged cos², before Malus ever enters
Open polarisation lab →
← Energy lost between two amplitudesMalus discipline →