Critical Angle⚠ unverified
Physics / Optics · Compute the critical angle for total internal reflection
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| n1 | n1 | — | 1.0 | Refractive index of the denser incident medium (dimensionless) |
| n2 | n2 | — | 1.0 | Refractive index of the less dense transmitting medium (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | θc | — | Critical angle, in degrees. Returns 0.0 when ``n1 <= n2`` (no critical angle exists) |
The science & history
Understanding the Parameters
- $n_2/n_1 < 1$ required; otherwise arcsin argument invalid (no TIR into denser medium).
- $\theta_c$ — glass→air ~42 deg; basis of optical fibers and prisms.
Derivation (Approaching a Proof)
Set $\theta_2 = 90^{\circ}$ in Snell’s law: $n_1\sin\theta_c = n_2$ ⇒ $\theta_c = \arcsin(n_2/n_1)$.
History
TIR was known to Kepler and others; critical angle is standard geometric optics.
Related Concepts: Snell's Law refraction angle, Brewster Angle, Numerical Aperture, Fresnel Reflection
Notes: Registry calculator critical-angle (unverified). Requires $n_1 > n_2$.