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.

Iin=25 W/m2359 W/m24514425 W/m2I_{\mathrm{in}}=25\ \text{W}/\text{m}^{2}\xrightarrow{\frac{3}{5}} 9\ \text{W}/\text{m}^{2}\xrightarrow{\frac{4}{5}} \tfrac{144}{25}\ \text{W}/\text{m}^{2}
Middle polarizer revives transmissionA middle axis applies exact ordered factors.stage0=25 W/m^2stage1=9 W/m^2stage2=144/25 W/m^2