Refractive Index Calculator: n = c/v and Snell's Law Method
The refractive index, n, characterises how much a transparent medium slows down light compared to its speed in vacuum. The fundamental definition is n = c/v, where c is the speed of light in vacuum (exactly 299,792,458 m/s by definition since 1983) and v is the phase velocity of light in the medium. Alternatively, n can be measured experimentally by applying Snell's Law: when light crosses a boundary at known angles of incidence and refraction, n = sin(theta_i) / sin(theta_r) gives the refractive index of the second medium relative to the first. The refractive index governs how lenses focus light, how much prisms disperse colours, and the critical angle for total internal reflection in optical fibres. It also underpins the design of anti-reflection coatings, immersion microscopy, and gemstone brilliance. This calculator supports both methods: enter a phase velocity to get n directly from n = c/v, or enter angles of incidence and refraction to determine relative n via Snell's Law. A reference table of common material values is included below.
Refractive index: --
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Refractive index formulas
From phase velocity
n = c / v
where c = 299,792,458 m/s (exact, NIST CODATA 2018) and v is the phase velocity of light in the medium. Rearranging: v = c / n.
From angles (Snell's Law method)
n = sin(θ_incidence) / sin(θ_refraction)
This gives the refractive index of the second medium relative to the first. If the first medium is air (n approximately 1.000), this is approximately the absolute refractive index of the second medium.
Reference refractive indices
| Material | n (589 nm, 20 °C) | Speed of light (km/s) |
|---|---|---|
| Vacuum | 1.000 000 (exact) | 299,792 |
| Air (STP) | 1.000 293 | 299,705 |
| Ice (0 °C) | 1.310 | 228,850 |
| Water (20 °C) | 1.333 | 224,900 |
| Ethanol | 1.361 | 220,300 |
| Fused silica (SiO2) | 1.458 | 205,600 |
| Crown glass | 1.520 | 197,200 |
| Flint glass | 1.620 | 185,000 |
| Sapphire (Al2O3) | 1.770 | 169,400 |
| Diamond | 2.417 | 124,000 |
| Silicon (infrared) | 3.480 | 86,100 |
Values are for the sodium D line at 589 nm. Refractive index varies with wavelength (dispersion) and temperature. Source: CRC Handbook of Chemistry and Physics; NIST Standard Reference Data.
Frequently asked questions
What does the refractive index mean physically?
The refractive index n of a medium is the ratio of the speed of light in vacuum (c = 299,792,458 m/s exactly) to the phase velocity of light in that medium: n = c/v. A value of n = 1.5 means light travels at two-thirds the speed it would in vacuum. Because n is always greater than or equal to 1 for passive materials, light always slows down when entering a transparent medium from vacuum.
Why does the refractive index matter in optics?
The refractive index determines how much light bends at a surface (via Snell's Law), how much a lens magnifies, the critical angle for total internal reflection in fibre optics, and how prisms split white light into a spectrum. Higher refractive index means stronger bending and a smaller critical angle. Lens designers combine glasses with different indices to correct chromatic and spherical aberration.
What is the relationship between refractive index and the speed of light?
The speed of light in a medium is v = c / n, where c = 299,792,458 m/s and n is the refractive index. In diamond (n approximately 2.42), light travels at about 124,000 km/s, compared to approximately 300,000 km/s in vacuum. In water (n approximately 1.33), light travels at roughly 225,000 km/s.
What is dispersion and why does it matter?
Dispersion is the variation of refractive index with wavelength. Glass refracts violet light (short wavelength) more than red light (long wavelength) because n is slightly higher at shorter wavelengths. This causes prisms to split white light into a rainbow spectrum and is the origin of chromatic aberration in simple lenses. Lens designers control dispersion by combining crown and flint glasses with different dispersion profiles.
Can the refractive index be less than 1?
For most transparent materials at optical frequencies, n is greater than 1. However, the phase refractive index of X-rays in some materials is very slightly less than 1, meaning X-rays can undergo total external reflection. Engineered metamaterials have been designed with negative refractive indices at microwave frequencies. These are exotic cases; for visible light in natural materials n is always greater than 1.