Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== 1. Dispersion → color dependence. n(λ) varies across visible wavelengths; that shifts the ray-deviation extremum D_min(λ) and so the scattering angle θ(λ). For water droplets this color shift is what produces the ~1–2° spread between red and blue in the rainbow’s radius; for other spherical surfaces (electron/light-sphere geometry) a similar dispersion-caused angular variation exists. ===
# Narrow lines can strongly bias the mean. If S(λ) is smoothly distributed (Planck), the mean will sit close to a spectrum-averaged θ(λ). But if S(λ) has strong narrow peaks (atomic emission lines like H-α 656.3 nm, H-β 486.1 nm, sodium D ~589 nm, or plasma lines), a narrow, strong line in a region where θ(λ) has a slightly different value will pull the mean more than a broad smooth Planck curve does.
# Plasma emission is important at astrophysical / stellar scales. Hot plasmas produce many emission lines (and continuum) at wavelengths where dispersion of the medium is significant. In QAT, if the geometry is probed by plasma light rather than a smooth blackbody, the effective observed angle can shift.
# Broken symmetry & statistical unfolding. If the QAT geometry is an ensemble process (broken spherical symmetry, many micro-events), then different micro-sources (each with their Sᵢ(λ)) average to a slightly shifted macroscopic effective angle. That statistical character can explain why the golden geometric angle and the physical 1/α are close but not exactly equal.