polarizer-chain-depth-three-row-scan - Electromagnetic Waves and Radiation Step by Step

A chain-depth scan varies the number of polarizers in the sequence across rows, showing how each added cos^2(theta) stage cuts the transmitted intensity further. The arithmetic is exact only for the stated chain depths, axis angles, and rows in the ideal lossless-polarizer model. Real beams add finite bandwidth, imperfect polarizers, alignment error, detector calibration, surface assumptions, and measurement uncertainty.

One, two, and three checked polarizer stages make the ordered intensity product explicit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One polarizer stage takes twenty-five to nine

One factor 3/5 turns source 25 watts per square metre into 9 watts per square metre.

25\ \text{W}/\text{m}^{2}\xrightarrow{\frac{3}{5}}9\ \text{W}/\text{m}^{2}

Two stages multiply in order

A second same factor starts from 9 watts per square metre and lands at 81/25 watts per square metre. The source is not reused; the stage output becomes the next input.

25\ \text{W}/\text{m}^{2}\xrightarrow{\frac{3}{5}}9\ \text{W}/\text{m}^{2}\xrightarrow{\frac{3}{5}}\tfrac{81}{25}\ \text{W}/\text{m}^{2}

Three stages show the continuing product

The third row appends factor 4/5 and reaches 1296/625 watts per square metre. The fractions stay exact rather than being rounded.

25\ \text{W}/\text{m}^{2}\to9\ \text{W}/\text{m}^{2}\to\tfrac{81}{25}\ \text{W}/\text{m}^{2}\to\tfrac{1296}{625}\ \text{W}/\text{m}^{2}