Refraction angle
Measured from the normal in medium 2.
Physics · Optics
Snell’s law refraction calculator
Enter the refractive indices and the incident angle measured from the normal, not the surface. The calculator distinguishes refraction, grazing transmission and total internal reflection.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Critical angle
Exists only for n₁ > n₂. Above θc there is total internal reflection.
Required sine ratio
r > 1 means no real refracted angle.
Relation and numerical substitution
n₁ sinθ₁ = n₂ sinθ₂—
Flat interface, homogeneous isotropic transparent media and geometrical optics. Indices correspond to the wavelength and conditions of the problem.
01Formulas and symbols
Formulas used
r
r = n₁ sinθ₁ / n₂Sine required by Snell’s law.θ₂
θ₂ = asin(r), 0 ≤ r ≤ 1Refracted angle when the required sine is at most one.θc
θc = asin(n₂/n₁), n₁ > n₂Critical incidence for passage from higher to lower refractive index.02Assumptions and limits
Scope of validity
- Flat interface, homogeneous isotropic transparent media and geometrical optics. Indices correspond to the wavelength and conditions of the problem.
03Validation example
Reference numerical case
- Given n₁ = 1, n₂ = 1.5, θ₁ = 30°: r = 1 × sin(30°)/1.5 = 1/3; θ₂ = asin(1/3) = 19.4712…° (≈ 19°).
- For n₁ = 1.5, n₂ = 1: θc = asin(1/1.5) = 41.8103…°. At θ₁ = 60°, r ≈ 1.299 > 1: total internal reflection.
04References
Technical references
FAQ
Why measure from the normal?
Snell’s law uses angles from the perpendicular to the interface. If an angle is measured from the surface, subtract it from 90°.
When does total internal reflection occur?
Only when n₁ > n₂ and θ₁ exceeds asin(n₂/n₁). At the critical angle the transmitted ray is grazing.
05Bending and the critical angle
Entering a higher-index medium bends the ray toward the normal. Entering a lower-index medium bends it away. A required sine above one is a physical change of regime, not a numerical angle.
06Model limits
No absorption, polarization, Fresnel power coefficients, anisotropy or material database is included. The diagram shows directions, not transmitted or reflected power.
07Common mistakes
Do not swap incident and transmitted indices. Do not replace a sine above one by one: that would falsely show a grazing ray instead of total reflection.