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

=== - Using a realistic Sellmeier-style n(λ)n(\lambda)n(λ) for water and the geometric primary-rainbow formula D(i)=2i−4r+πD(i)=2i-4r+\piD(i)=2i−4r+π (with sin⁡i=nsin⁡r\sin i = n\sin rsini=nsinr) I computed Dmin⁡(λ)D_{\min}(\lambda)Dmin(λ) across the visible band and then formed spectrum-weighted averages. ===
* For a Sun-like blackbody (Planck T=5800T=5800T=5800 K) the Planck-weighted mean minimum-deviation is Dmean(5800 K)≈138.09∘\mathbf{D_{\rm mean}(5800\,\mathrm{K}) \approx 138.09^\circ}Dmean(5800K)≈138.09∘. That sits above the golden angle number you used (137.5078°) and above the inverse fine-structure number (≈137.036).
* Changing the spectral weighting (i.e. the effective source temperature) moves the weighted mean continuously: • to hit the golden angle (137.5078°) the continuum would correspond to ≈3765 K (cooler than the Sun), • to hit 1/α≈137.0361/\alpha\approx137.0361/α≈137.036 you’d need ≈2068 K (much cooler).
* Narrow emission lines (Hα, Hβ, Na D, [O III], etc.) do move the weighted mean but only by a small amount unless their integrated power is unrealistically large compared with the continuum. In other words, narrow lines alone (at realistic strengths) are unlikely to explain a 0.47° offset.

Conclusion: yes — spectral weighting (a different effective source temperature or very different spectral shape) can change the average rainbow angle by a few tenths of a degree — so in principle a spectral explanation for a ~0.47° offset is possible — but you need a fairly different spectrum (not just a few weak lines) or the effect of additional physics (Mie scattering amplitude + droplet size distribution) to match the tiny offset robustly.