Input interpretation
rainbow altitude
Equation
θ = δ - ϕ | δ = 4 θ_r - 2 θ_i sin(θ_i) = n_w sin(θ_r) | cos^2(θ_i) = 1/3 (n_w^2 - 1) | θ | altitude of rainbow ϕ | altitude of sun δ | angle of deviation θ_r | angle of refraction θ_i | angle of incidence n_w | index of refraction (for top edge of primary bow)
Input value
altitude of sun | 39.1822° (degrees)
Result
altitude of rainbow | 2.896° (degrees) = 50.54 mrad (milliradians) = 0.05054 radians = 2 degrees 53 arc minutes 45.22 arc seconds
Rainbow properties
bow order | altitude | angular width 1st | 2.896° (degrees) | 2.383° (degrees) 2nd | 15.06° (degrees) | 3.88° (degrees) 3rd | 103.8° (degrees) | 5.234° (degrees) (altitude to upper edge; angles above 90° are behind viewer)
Schematic
Schematic
Rainbow altitude vs. sun altitude
Rainbow altitude vs. sun altitude
Raindrop schematic
Raindrop schematic