Malus discipline
● VERBATIM — examined word-for-wordI = I₀cos²θ applies only to already-polarised light; θ is between the light's polarisation plane and the analyser axis — i.e. between consecutive axes, computed from geometry, never the printed angle to the vertical (axis 40° to horizontal + vertically polarised light → θ = 50°). Chains: multiply cos²θ per filter, amplitude (A ≡ y₀ throughout) picks up cosθ per filter.
I = I₀cos²θ · A = A₀cosθWhat this actually means
Malus' law applies only to light that is already polarised. The angle θ is between the light's current polarisation plane and the next axis it meets, in other words between consecutive axes.
The printed angle is usually measured to the vertical or horizontal, which is rarely the angle you need. Vertically polarised light meeting an axis at 40° to the horizontal: θ = 50°.
Chains multiply: another factor of cos²θ per filter for intensity, and a single factor of cosθ per filter for amplitude.
Using the printed angle to the vertical instead of the angle between consecutive axes.
Prove it — watch it be true
- Set the polariser at θ₁ and the analyser at θ₂
- Watch the live cos² curve: the input is the angle BETWEEN them
- Rotate both together: intensity unchanged, because their difference did not change