Snell's Law (refraction angle)⚠ unverified
Physics / Optics · Refraction angle from Snell's law (angles in radians)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| n1 | n1 | — | 1.0 | Index of incident medium |
| n2 | n2 | — | 1.5 | Index of refracting medium |
| theta1 | θ1 | rad | 0.5236 | Angle of incidence |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| theta2 | θ2 | rad | Angle of refraction |
The science & history
Understanding the Parameters
- $n_1$, $n_2$ — absolute indices (vacuum $n=1$, glass ~1.5). Relative index $n_1/n_2$ sets the bend.
- $\theta_1$ — must be in radians for most solvers (e.g. 0.524 ≈ 30 deg).
- $\theta_2$ — bends toward the normal when entering higher $n$.
Derivation (Approaching a Proof)
Phase matching / Fermat’s principle along the interface requires continuity of the tangential wave vector: $n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2$, hence Snell’s law. Solving for $\theta_2$ gives the arcsin form.
History
Snell (1621) and Descartes; foundational for lenses, fiber optics, and atmospheric refraction.
Related Concepts: Critical Angle, Brewster Angle, Fresnel Reflection, Optical Path Length
Notes: Registry calculator snells-law (unverified). Real arcsin domain only (no TIR handling beyond failure).