Rainbow Formation

Display

Impact parameter b: 0.86 (0=center, 1=edge) Wavelength: 550 nm

Raindrop Properties

Refractive index n (water): 1.333 Drop radius R: 1.0 mm

Angles

—

θ_r refraction

—

D deviation

—

Rainbow angle

—

D_min (°)

Descartes Formula

sin(θᵢ) = b (normalized)
sin(θᵣ) = sin(θᵢ)/n

D(b) = 2θᵢ − 4θᵣ + π
(1° internal reflection)

D_min at dD/db = 0:
cos(θᵢ) = √((n²−1)/3)

Primary bow: D_min ≈ 138°
Seen at 180°−D_min ≈ 42°
Secondary (2 reflections): ≈ 51°