How this calculator works
An analyser passes the electric-field component parallel to its transmission axis. Intensity is proportional to field amplitude squared, producing a cosine-squared dependence. The angle inverse returns the acute solution between 0 and 90 degrees; other orientations repeat periodically. Unpolarized light loses half its intensity at a first ideal polarizer before Malus law applies to later analysers.
Formula
I = I0 cos²θ; θ = acos(sqrt(I/I0)); I0 = I/cos²θ when cosθ is non-zero.
Worked example
An initial polarized intensity of 100 W/m2 at 60 degrees gives 25 W/m2 after the analyser. At 45 degrees it gives 50 W/m2.
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Frequently asked questions
What happens at 90 degrees?
Ideal crossed axes transmit zero. Real polarizers have finite extinction ratios.
Can I start with unpolarized light?
First halve its intensity for an ideal initial polarizer, then use the angle between subsequent polarization axes.
Why is an angle above 90 degrees unnecessary?
The intensity repeats with a 180-degree period and is symmetric about 90 degrees.