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

=== This calculation purposely kept things simple (so you can follow the logic and we can iterate quickly). Important limitations you should know: ===
# Dispersion model is approximate. I used a simple analytic form for n(λ). Real water dispersion (especially over the visible) is known precisely in the literature (Hale & Querry; refractiveindex.info). Small refractive-index differences (10⁻³ level) change the stationary deviation by fractions of a degree — so accurate n(λ) is crucial.
# Line strengths & real spectral shapes matter. I used Gaussian lines with arbitrary amplitudes. Real astrophysical or plasma emission line strengths (and stellar continua) have very different relative intensities. A sufficiently strong narrow line inside a region where θ(λ) changes rapidly could pull the mean by a small amount — but you must use realistic amplitudes.
# Scattering intensity vs geometric deviation. The physically observed rainbow brightness at a given angle is not just where the stationary deviation occurs; it depends on the intensity distribution (Airy interference pattern, droplet size, polarization). To predict what an observer measures (and therefore the “effective” angle) properly you must weight by scattering intensity, not just spectral power. Wave-optics corrections (Mie/Airy) for finite droplet sizes can shift and shape the observed maximum by tenths of a degree.
# Range and normalization. I integrated over 350–900 nm with unadjusted absolute Planck radiances. Different normalization or detection sensitivity curves (e.g., human eye sensitivity, instrument response) will change the weighted mean.
# Plasma bremsstrahlung / continuum, particulate scattering, and droplet size distribution can all change the final observed angular distribution.
# Order of magnitude: the ~0.47° offset is fairly small; matching that precisely will likely need precise input data (accurate n(λ), correct emission line strengths, instrument or eyeball response, and correct wave-optics scattering weighting).