Snell's Law Calculator

Snell's Law describes how light bends (refracts) when it crosses the boundary between two media with different refractive indices. The formula is n₁·sin(θ₁) = n₂·sin(θ₂), where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal to the boundary. See also our calculate Laser Pulse Peak Power.

Yes — Snell's Law applies to any wave crossing a boundary between two media where the wave speed changes, including sound waves and seismic waves. However, it is most commonly used for light (electromagnetic waves) in optics. The principle of refraction is universal wherever wave speed changes at an interface.

The critical angle (θc) is the minimum angle of incidence — measured from the normal — at which light traveling from a denser medium to a less dense medium is completely reflected back rather than refracted. Above this angle, no refraction occurs and Total Internal Reflection (TIR) takes place. The critical angle is given by θc = arcsin(n₂/n₁) and only exists when n₁ > n₂.

Using Snell's Law with n₁ = 1.0003 (air) and n₂ = 1.333 (water): sin(θ₂) = (1.0003/1.333)·sin(30°) = 0.7511 × 0.5 ≈ 0.3756. Therefore θ₂ = arcsin(0.3756) ≈ 22.05°. Light bends toward the normal when entering a denser medium. You might also find our calculate Optical Path Difference (OPD), Reflectivity R & Refraction Angle θ₂ in Film — Thin-Film Optical Coating useful.

If you know the angle of incidence (θ₁) in air (n₁ ≈ 1.0003) and the measured angle of refraction (θ₂) in the glass, rearrange Snell's Law to get n₂ = n₁·sin(θ₁)/sin(θ₂). For example, if θ₁ = 45° and θ₂ = 28°, then n₂ = 1.0003 × sin(45°)/sin(28°) ≈ 1.505, consistent with crown glass.

Snell's Law assumes the media are isotropic (uniform in all directions), homogeneous, and that the interface is flat and smooth. It does not account for effects like dispersion (different wavelengths bending by different amounts), birefringence in anisotropic crystals, or wave phenomena like diffraction. At very high intensities, nonlinear optical effects can also cause deviations.

The refractive index n of a medium is the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v): n = c/v. A higher refractive index means light travels more slowly through the material. Vacuum has n = 1.0 (by definition), water is about 1.333, and diamond is about 2.417, meaning light travels at roughly 41% of its vacuum speed inside a diamond.

Angles are measured from the normal (the line perpendicular to the interface) because the geometry of refraction is symmetric with respect to this perpendicular line, not the surface itself. Using the normal as reference makes the mathematical relationship between incoming and outgoing rays consistent regardless of how the interface is oriented in space.