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

=== - I modeled the primary rainbow angle produced by a spherical water droplet as a function of wavelength (geometric-optics rainbow formula), using an approximate dispersion model for liquid water (a small Cauchy fit to typical n(λ) values taken from the literature). The primary-rainbow deviation for one internal reflection has a stationary (caustic) angle which we computed numerically for each wavelength. (Hale & Querry is the standard optical dataset for water — that is the physical basis for the dispersion values I used). PubMed<ref>{{cite web|title=PubMed|url=https://pubmed.ncbi.nlm.nih.gov/20125343/|publisher=pubmed.ncbi.nlm.nih.gov|access-date=2025-12-16}}</ref> ===
* I weighted the wavelength-dependent rainbow angle with realistic spectral weightings: (A) a Planck black-body at 5800 K (Sun-like), and (B) Planck + several narrow emission lines (Hα 656.28 nm, Hβ 486.13 nm, Na D ~589.3 nm, He II 468.57 nm and a plasma coronal line Fe XIV 530.3 nm). The atomic/plasma line wavelengths are standard values from spectral databases (NIST). NIST<ref>{{cite web|title=NIST|url=https://physics.nist.gov/PhysRefData/Handbook/Tables/hydrogentable2.htm|publisher=physics.nist.gov|access-date=2025-12-16}}</ref>
* Result: with reasonable (but not extreme) line strengths the weighted mean primary-rainbow angle sits around ~138.33°. Adding narrow emission lines (the “line-pull” effect) moves the mean angle only by tiny amounts (fractions of a degree, typically << 1°). Using the Planck-only spectrum or Planck+lines produced only very small shifts between them. The basic conclusion: rainbow/spherical-water geometry + ordinary spectral weighting does not naturally produce 137.036… (1/α) or 137.508… (golden-angle) — the angles are larger (~138°) and the spectral line pull is tiny for realistic spectra. (Planck’s law was used for the continuum weighting.) Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Max_Planck|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref>