Refractive Index Calculator

Calculate refractive index n = c/v from light speed in medium, look up n for 50+ materials, or derive from angles via Snell's Law. Includes critical angle, Brewster's angle, and Abbe number.

Refractive Index n
—
Speed in Medium (m/s) —
Material / Source —
Extended More scenarios, charts & detailed breakdown ▾
Refractive Index n = c/v
—
Speed Ratio v/c —
Professional Full parameters & maximum detail ▾

Optical Properties

n_d (589 nm yellow) —
Abbe Number V_d —
Speed in Medium (×10⁶ m/s) —

Special Angles

Critical Angle vs Air (degrees) —
Brewster's Angle vs Air (degrees) —

How to Use This Calculator

  1. Select calculation mode: Speed of Light (enter v in the medium), Material Lookup (select from list), or Snell's Angles (enter both angles).
  2. Enter the required inputs.
  3. Results show refractive index, speed in medium, and critical angle vs air.
  4. Use Professional for Abbe number and dispersion data for common optical glasses.

Formula

n = c / v (c = 299,792,458 m/s)

From Snell's Law: n₂ = n₁ sin θ₁ / sin θ₂

Critical angle: θ_c = arcsin(1/n) vs air

Brewster's angle: θ_B = arctan(n)

Example

Example: Light in crown glass travels at 1.975 × 10⁸ m/s. n = 2.998×10⁸ / 1.975×10⁸ = 1.518 (matches crown glass BK7). Critical angle vs air = arcsin(1/1.518) = 41.1°.

Frequently Asked Questions

  • n = c/v, where c = speed of light in vacuum (299,792,458 m/s) and v = speed of light in the medium. n ≥ 1 always (light can't travel faster than c in vacuum). Higher n means slower light and more bending at interfaces.
  • Higher n: light travels slower, bends more at interfaces (stronger Snell refraction), higher critical angle needed for TIR, more reflective (Fresnel). Diamond (n = 2.42) sparkles because of multiple TIR reflections inside it.
  • Abbe number V_d = (n_d − 1)/(n_F − n_C) measures dispersion across the visible spectrum. Low V_d (flint glass ≈ 36) = high dispersion = more chromatic aberration. High V_d (crown glass ≈ 64) = low dispersion. Achromatic lenses pair high/low V_d glasses.
  • At Brewster's angle θ_B = arctan(n₂/n₁), reflected light is perfectly polarized (only s-polarization). Used in polarized camera filters, laser windows (Brewster windows), and LCD displays to reduce glare.
  • Yes — dispersion. Blue light (shorter wavelength) bends more than red (longer wavelength) in glass. This splits white light into a spectrum (prism). The Cauchy/Sellmeier equations model n(λ). The Abbe number summarizes this over the visible range.

Related Calculators

🔆 Snell's Law Calculator 🌀 Critical Angle Calculator ⚙️ Lensmaker's Equation 🌊 Wavelength Calculator
Sources & References (5) ▾
  1. refractiveindex.info — Optical Constants Database — refractiveindex.info
  2. NIST Optical Constants of Materials — NIST
  3. Hecht, E. Optics (5th ed.) — Pearson
  4. Schott Optical Glass Data Sheets — Schott AG
  5. HyperPhysics — Refractive Index — Georgia State University