Two crossed polarizers block the beam, but inserting a middle polarizer at an intermediate angle opens a path: each stage applies its own cos^2(theta) factor via Malus's law and a nonzero intensity gets through. The arithmetic is exact only for ideal lossless polarizers with stated axis angles and input intensity. Real beams add finite bandwidth, imperfect polarizers, alignment error, detector calibration, and measurement uncertainty.
A middle axis can route light through crossed polarizers in this checked chain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A middle polarizer can revive a crossed pair
A middle axis with factor 3/5 from the first and 4/5 from the second gives a nonzero final stage.