Polarization Boundary and Invariant Scans

Wave Speed Consistency Three-Row Scan

A wave-speed-consistency scan varies wavelength and frequency together across three rows, checking that c = lambda * f stays constant row by row. The arithmetic is exact only for the stated wave speeds, wavelengths, frequencies, and rows in the ideal uniform-wave model. Real measurements add bandwidth, alignment, detector calibration, polarizer extinction ratio, material dispersion/loss, finite precision, and measurement uncertainty.

Three exact rows keep E=cB and wavelength-frequency speed consistent. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The same magnetic field and frequency set a new speed row

Magnetic amplitude and frequency stay fixed. The checked wave row moves electric field and wavelength together so both speed ledgers agree.

E=cB=4 m/s⋅2 T=8 V/mλf=2 m⋅2 Hz=4 m/s\begin{array}{c}E=cB=4\ \text{m}/\text{s}\cdot2\ \text{T}=8\ \text{V}/\text{m}\\\lambda f=2\ \text{m}\cdot2\ \text{Hz}=4\ \text{m}/\text{s}\end{array}
Wave speed consistency rowBoth speed equations are bound to the same wave source.speed=4 m/smagneticField=2 TelectricField=8 V/mwavelength=2 mfrequency=2 Hz

The same magnetic field and frequency set a new speed row

Magnetic amplitude and frequency stay fixed. The checked wave row moves electric field and wavelength together so both speed ledgers agree.

E=cB=6 m/s⋅2 T=12 V/mλf=3 m⋅2 Hz=6 m/s\begin{array}{c}E=cB=6\ \text{m}/\text{s}\cdot2\ \text{T}=12\ \text{V}/\text{m}\\\lambda f=3\ \text{m}\cdot2\ \text{Hz}=6\ \text{m}/\text{s}\end{array}
Wave speed consistency rowBoth speed equations are bound to the same wave source.speed=6 m/smagneticField=2 TelectricField=12 V/mwavelength=3 mfrequency=2 Hz

The same magnetic field and frequency set a new speed row

Magnetic amplitude and frequency stay fixed. The checked wave row moves electric field and wavelength together so both speed ledgers agree.

E=cB=8 m/s⋅2 T=16 V/mλf=4 m⋅2 Hz=8 m/s\begin{array}{c}E=cB=8\ \text{m}/\text{s}\cdot2\ \text{T}=16\ \text{V}/\text{m}\\\lambda f=4\ \text{m}\cdot2\ \text{Hz}=8\ \text{m}/\text{s}\end{array}
Wave speed consistency rowBoth speed equations are bound to the same wave source.speed=8 m/smagneticField=2 TelectricField=16 V/mwavelength=4 mfrequency=2 Hz