Snell's Law Optical Refraction Calculator
Snell's Law governs the bending of light rays across an interface between two isotropic media with refractive indices n₁ and n₂: n₁ × sin(θ₁) = n₂ × sin(θ₂).
Transmitted ray angle from normal in degrees
Index of refraction of medium 1 (Air = 1.0003)
Incident ray angle from surface normal in degrees
Index of refraction of medium 2 (Water = 1.333, Glass = 1.50)
Step-by-Step Calculation
Snell's Law governs the bending of light rays across an interface between two isotropic media with refractive indices n₁ and n₂: n₁ × sin(θ₁) = n₂ × sin(θ₂).
Real-World Reference Values
Phase velocity equals c
Standard optical lens substrates
Critical angle in air θ_c = 24.4°
20-Row Comparison Table
Angle of Refraction (θ₂ (°)) · Incident Refractive Index (n₁)
| # | Incident Refractive Index (n₁) | Angle of Refraction (θ₂ (°)) | Δ % |
|---|---|---|---|
| 01 | 1 Current | 28.1255 | 0.00% |
| 02 | 1.0405 | 29.374 | +4.44% |
| 03 | 1.0811 | 30.6381 | +8.93% |
| 04 | 1.1216 | 31.9188 | +13.49% |
| 05 | 1.1621 | 33.2177 | +18.11% |
| 06 | 1.2026 | 34.5361 | +22.79% |
| 07 | 1.2432 | 35.8758 | +27.56% |
| 08 | 1.2837 | 37.2385 | +32.40% |
| 09 | 1.3242 | 38.6263 | +37.34% |
| 10 | 1.3647 | 40.0416 | +42.37% |
| 11 | 1.4053 | 41.4868 | +47.51% |
| 12 | 1.4458 | 42.965 | +52.76% |
| 13 | 1.4863 | 44.4797 | +58.15% |
| 14 | 1.5268 | 46.0347 | +63.68% |
| 15 | 1.5674 | 47.6348 | +69.37% |
| 16 | 1.6079 | 49.2855 | +75.23% |
| 17 | 1.6484 | 50.9934 | +81.31% |
| 18 | 1.6889 | 52.7666 | +87.61% |
| 19 | 1.7295 | 54.6152 | +94.18% |
| 20 | 1.77 | 56.552 | +101.07% |
Frequently Asked Questions
How do I find the Critical Angle for Total Internal Reflection?+
Lock θ₁ (°), set θ₂ = 90° (or 89.9°), and enter n₁ > n₂ (e.g., n₁ = 1.50 glass to n₂ = 1.00 air). The resulting θ₁ is the critical angle.
Why does light bend toward the normal when entering a denser medium?+
Because phase velocity slows down (v = c / n), the wavefront pivots toward the normal so that sin(θ₂) < sin(θ₁).
How are angles θ₁ and θ₂ measured?+
In optics, both angles are measured relative to the perpendicular surface normal, not the flat interface surface.