A chain of polarizers multiplies the intensity by a cos^2 factor for each angle between consecutive axes, so the sequence is an ordered ledger. Reordering the polarizers changes the intermediate angles and so changes the final intensity. The product rule is exact for ideal lossless elements with stated axis angles; real setups add leakage, absorption, alignment error, and detector noise at every stage.

Two ordered stages multiply the source irradiance by each factor in turn. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two polarizers multiply by their factors in order

Stage by stage multiplication uses the same checked source order: 25 watts per square metre

stagestart=25 W/m2→359 W/m2→→358125 W/m2\text{stage}_\text{start}=25\ \text{W}/\text{m}^{2}\xrightarrow{\frac{3}{5}} 9\ \text{W}/\text{m}^{2}\to \xrightarrow{\frac{3}{5}} \tfrac{81}{25}\ \text{W}/\text{m}^{2}
Polarizers in orderThe ordered chain enforces structural factor order.stage0=25 W/m^2stage1=9 W/m^2stage2=81/25 W/m^2