Light passes a polarizer, then a rotatable analyzer. The transmitted intensity follows I = I0·cos²(angle) — and an unpolarized source loses half its intensity at the first filter before that law even starts.
Transmitted intensity I = I0·cos²
375 W/m²
Partial transmission.
The numbers
Share of I0 transmitted75.0%
cos² of the angle0.750
Reaching the analyzer500 W/m²
Incident intensity I0500 W/m²
Analyzer angle30°
Unpolarized light keeps only half its intensity at the first filter (whatever its angle); already-polarized light obeys Malus's law directly. Crossed axes (90°) block everything.
Tip: sweep the angle slowly — half the light is still passing at 45°, and true darkness only arrives at a full 90°.