Impulse-Projection Cross-Scan - Electromagnetic Waves and Radiation Step by Step

An impulse-projection cross-scan varies the incidence angle across rows, showing how the cos(theta) projection scales both the effective area and the delivered impulse J = F * t * cos(theta). The arithmetic is exact only for the stated irradiance, area, time, and angles in the ideal uniform-beam, flat-surface model. Real measurements add beam profile, alignment, reflectivity/absorption, detector calibration, timing/area calibration, surface geometry, and uncertainty.

Impulse is scanned across time and projection across normal 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

Impulse accumulates force over a finite time

The impulse ledger uses a force source and a finite time window. The units are momentum units by construction.

J=Ft=3\cdot4=12\ \text{kg}\,\text{m}/\text{s}

Longer time gives larger impulse

Force is fixed in these rows. The impulse column changes only with the finite time window.

\begin{array}{c|c|c}F&t&J\\3\ \text{N}&2\ \text{s}&6\ \text{kg}\,\text{m}/\text{s}\\3\ \text{N}&4\ \text{s}&12\ \text{kg}\,\text{m}/\text{s}\\3\ \text{N}&6\ \text{s}&18\ \text{kg}\,\text{m}/\text{s}\\\end{array}

Normal projection gates the usable irradiance

Projection is a bounded exact factor in this training surface. The half-projection row matches the rendered projection case.

\begin{array}{c|c|c}q&I&I_\perp\\0&6\ \text{W}/\text{m}^{2}&0\ \text{W}/\text{m}^{2}\\\frac{1}{2}&6\ \text{W}/\text{m}^{2}&3\ \text{W}/\text{m}^{2}\\1&6\ \text{W}/\text{m}^{2}&6\ \text{W}/\text{m}^{2}\\\end{array}