Find a material’s refractive index. This free calculator uses Snell’s law (from the angles of incidence and refraction) or the speed of light (n = c/v), and shows the critical angle too.
Refractive index of the second medium from Snell’s law: n₂ = n₁ · sin θ₁ / sin θ₂. Angles are measured from the normal.
Refractive index from the speed of light: n = c / v, where c = 299,792,458 m/s (speed of light in a vacuum).
For reference: vacuum 1.0000, air ≈ 1.0003, water ≈ 1.333, typical glass ≈ 1.5, diamond ≈ 2.42. The refractive index has no units.
How the Refractive Index Calculator Works
The refractive index describes how much a material bends and slows down light compared to a vacuum. This calculator finds it two ways: from the angles light makes as it crosses a boundary (Snell’s law), or directly from the speed of light measured inside the material.
Formula: Snell’s law mode: n2 = n1 × sin(θ1) ÷ sin(θ2), where θ1 and θ2 are measured from the normal to the surface. Speed mode: n = c ÷ v, where c = 299,792,458 m/s is the speed of light in a vacuum and v is the measured speed of light in the medium. When two refractive indices are known, the critical angle for total internal reflection is θc = arcsin(n_lower ÷ n_higher), valid only when light travels from the denser (higher-n) medium toward the less dense one.
- n₠— refractive index of the incident medium (the “nâ‚” field; leave blank to use air ≈ 1.00).
- θ₠— angle of incidence, entered in the “Angle of incidence θₔ field, measured in degrees from the normal.
- θ₂ — angle of refraction, entered in the “Angle of refraction θ₂” field, measured in degrees from the normal.
- v — speed of light inside the medium, entered in the “Speed of light in the medium (v)” field when using speed mode instead of Snell’s law.
Example Scenarios
| n₠(incident medium) | θ₠(incidence) | θ₂ (refraction) | n₂ (refractive index) |
|---|---|---|---|
| 1.00 | 45° | 28° | ≈1.51 |
| 1.00 | 60° | 40° | ≈1.35 |
| 1.00 | 50° | 30° | ≈1.53 |
| 1.00 | 35° | 23° | ≈1.47 |
| 1.00 | 20° | 13° | ≈1.52 |
| 1.00 | 70° | 24° | ≈2.31 |
Refractive Index Calculator FAQ
What does the refractive index actually measure?
It’s the ratio of how fast light travels in a vacuum compared to how fast it travels through a given material. A higher refractive index means light slows down and bends more when entering that material, which is why glass (≈1.5) bends light more than water (≈1.33).Why does the calculator ask for two different angles in Snell’s law mode?
Snell’s law relates the angle of incidence (in the first medium) to the angle of refraction (in the second medium). You need both, plus the first medium’s known refractive index, to solve for the unknown refractive index of the second medium.How is the critical angle for total internal reflection calculated?
The critical angle is arcsin of the lower refractive index divided by the higher one. It only applies when light is moving from a denser medium into a less dense one; beyond that angle, light reflects entirely instead of refracting through the boundary.What’s the difference between the Snell’s law method and the speed method?
Snell’s law mode calculates refractive index from measured angles at a boundary between two media. Speed mode calculates it directly from n = c/v if you already know how fast light travels through the material, without needing any angle measurements.Can the refractive index of a medium be less than 1?
For ordinary transparent materials like glass, water and air, no — the phase velocity of light in the material is always less than c, so n is always greater than or equal to 1. Values below 1 only show up in unusual physics contexts like certain plasmas or metamaterials.Why is air’s refractive index treated as approximately 1 instead of exactly 1?
Air is very close to a vacuum optically, but not identical — its refractive index is about 1.0003 at standard conditions. The calculator lets you leave n₠blank to default to 1.00 for simplicity, which is accurate enough for most everyday calculations.Related Calculators
Working through optics problems often means juggling angles as well as indices — the triangle calculator can help resolve related angle geometry. If your next step involves the light itself rather than the boundary it crosses, try the wavelength and frequency calculator or the speed of sound calculator for comparing wave behavior across different media.