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

=== I can run the numerical calculation for you (and publish the short results), and here’s the recommended pipeline: ===
# Choose a high-accuracy refractive-index dataset n(λ) for the material that best represents your “sphere”: • For raindrop test: use Hale & Querry or refractiveindex.info water data (tabulated n(λ) from 350–700 nm). • For atomic/electron-sphere: choose an effective dielectric model (or vacuum n=1 plus the interaction geometry you want to model).
# For each wavelength λ in the chosen range: a. compute n(λ), b. numerically find θᵢ that extremizes the deviation D(θᵢ; n(λ)) (solve dD/dθᵢ = 0), c. compute θ(λ) = 180° − D_min(λ).
# Choose S(λ) options: • Planck curves at relevant T values, • A handful of atomic lines: e.g., hydrogen Balmer lines (486, 656 nm), sodium D (~589 nm), He II lines (if plasma), • Plasma emission templates (if you want astrophysical plasma, choose representative strong lines).
# Compute weighted means θˉ\bar\thetaθˉ for each S(λ) case and evaluate Δθ relative to θ_G.
# Sensitivity scan: change relative amplitude of lines A_i and line width σ_i to see the amplitude of shift: how strong/dominant must a line be to give Δθ ≈ 0.47°?
# Use high-precision n(λ) tables (Hale & Querry or refractiveindex.info) to ensure accuracy.

If you want, I will run this numerically for you. I will:
• fetch refractiveindex.info / Hale & Querry tables (I’ll cite sources),
• implement the deviation formula and stationary point solver,
• compute θ(λ) across 350–900 nm,
• compute weighted means for Planck and selected line mixes,
• present a small plot and the numeric Δθ results.

Would you like me to run that calculation now? (If yes, confirm you want the water/rainbow geometry test first, and say which lines/temperatures to try — e.g., Planck at 5800 K (Sun), plus Hα, Hβ, Na D, and one example plasma line set.)