malus-factor-three-row-scan - Electromagnetic Waves and Polarization Step by Step

Changing the projection factor while holding source intensity fixed shows why intensity squares the field factor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Projection factor one keeps all intensity

Source intensity is 25 watts per square metre. Squaring factor 1 keeps transmitted intensity at 25 watts per square metre.

I_{\mathrm{out}}=25\ \text{W}/\text{m}^{2}\left(1\right)^{2}=25\ \text{W}/\text{m}^{2}

Factor four-fifths transmits sixteen

Changing only the projection factor to 4/5 sends the same source to 16 watts per square metre because intensity uses the squared factor.

I_{\mathrm{out}}=25\ \text{W}/\text{m}^{2}\left(\frac{4}{5}\right)^{2}=16\ \text{W}/\text{m}^{2}

Factor three-fifths transmits nine

The third factor is 3/5. It passes 9 watts per square metre and blocks 16 watts per square metre, so the squared relation is visible.

I_{\mathrm{out}}=25\ \text{W}/\text{m}^{2}\left(\frac{3}{5}\right)^{2}=9\ \text{W}/\text{m}^{2}