Physics Deep Dive
How Light Bends Through a Prism
When a ray of white light strikes the surface of a glass prism, it crosses a boundary between two media of different optical density — air (n ≈ 1.00) and glass (n ≈ 1.52). At this boundary, light slows down and bends toward the normal. This bending is called refraction, governed by Snell's Law:
n₁ sin θ₁ = n₂ sin θ₂ // Snell's Law at each face
θ_r = arcsin( (n₁/n₂) × sin θ_i ) // solving for refracted angle
δ = (i − r₁) + (e − r₂) // total angle of deviation
θ_r = arcsin( (n₁/n₂) × sin θ_i ) // solving for refracted angle
δ = (i − r₁) + (e − r₂) // total angle of deviation
At the second face the ray exits the glass — bending away from the normal back into air. The angular difference between the original incident direction and the final emergent ray is the angle of deviation (δ).
Why colours separate
Glass is a dispersive medium — refractive index varies with wavelength. Violet (400 nm) n ≈ 1.531 bends most. Red (700 nm) n ≈ 1.510 bends least. This is dispersion.
The Normal Line
The normal is perpendicular to the prism face at the point of incidence. All Snell's Law angles — θ₁ and θ₂ — are measured from this normal, not from the surface itself.
Angle of Deviation
The angle of deviation (δ) is the angle between the original incident ray and the final emergent ray. It reaches a minimum at the angle of minimum deviation.
Cauchy's Equation
Wavelength-dependence: n(λ) = A + B/λ². For borosilicate glass, A ≈ 1.5046, B ≈ 4200 nm² — used directly in this simulation for each spectral ray.
Visible Spectrum — Refractive Indices (Borosilicate Glass)
| Colour | λ (nm) | n(λ) | Bending |
|---|---|---|---|
| Red | 700 | 1.5100 | Least ↓ |
| Orange | 620 | 1.5140 | ↑ |
| Yellow | 589 | 1.5170 | ↑ |
| Green | 530 | 1.5200 | ↑ |
| Blue | 470 | 1.5240 | ↑ |
| Indigo | 440 | 1.5270 | ↑ |
| Violet | 400 | 1.5310 | Most ↑ |
Each wavelength follows its own Snell's Law computation, producing the rainbow fan emerging from the second prism face. Drag the slider to see how the angle of incidence changes the spread and deviation of all colours simultaneously.