Newton's prism - 2D ray-trace bench

Refraction and dispersion

At each glass face light obeys Snell's law, n₁ sin θ₁ = n₂ sin θ₂, and the refractive index depends on wavelength. Here n(λ) comes from the Sellmeier equation n² = 1 + Σ B_iλ² / (λ² - C_i) with the published coefficients of each glass. Blue light has the larger index and bends more, so a white beam fans out into a spectrum. This is the observation Newton made in 1666.

The prism

For a wedge of apex angle A the ray angles satisfy θ₂ = asin(sin θ₁ / n), θ₃ = A - θ₂, sin θ₄ = n sin θ₃, and the total deviation is δ = θ₁ + θ₄ - A. The deviation is smallest when the ray crosses symmetrically: n = sin((A + δ_min)/2) / sin(A/2). If n sin θ₃ exceeds 1 the ray cannot leave: total internal reflection. The Abbe number V_d = (n_d - 1)/(n_F - n_C) measures how weakly a glass disperses.

Honest simplifications: a single ray per wavelength through the middle of a sharp-edged wedge; no Fresnel reflection losses, absorption, diffraction or beam width; the on-screen colours are approximate display colours for each wavelength. Real crown glass spreads the spectrum by only about a degree, so the dispersion exaggeration slider scales (n - n_d) to make the fan visible; set it to 1 for the real glass.

• Sweep the incidence angle and watch the fan: it narrows and the beam deviation reaches a minimum, which the first graph marks.
• Raise the incidence angle or the apex angle until the violet, then the red ray, no longer leaves the prism: total internal reflection.
• Compare fused silica, BK7 and dense flint at exaggeration 1 and read the spectrum width.
• Move the hit position along the face: the angles do not change, only the geometry.