AkCalculators

Refractive Index — definition, formula, and optical insights

The refractive index (symbol n) quantifies how much light slows down when entering a material from vacuum. It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v):

n = c / v

Where c = 3 × 10⁸ m/s. For air at standard conditions, n ≈ 1.0003; for water n ≈ 1.33; for glass n ranges between 1.45 and 1.9 depending on type and wavelength.

How to use this calculator

• If you know the speed of light in a medium, compute n as c/v.
• If you know n, compute the light speed as v = c/n.
• Optionally, enter a wavelength (in nm) to estimate slight dispersion (n increases for shorter λ).
• Relative refractive index (n₂₁) = n₂ / n₁ helps evaluate refraction between two media.

Worked examples

Example 1 — Find n for glass: Light speed in glass is 2 × 10⁸ m/s. n = c/v = (3×10⁸)/(2×10⁸) = 1.5.

Example 2 — Speed in water: n = 1.33 ⇒ v = 3×10⁸ / 1.33 ≈ 2.26×10⁸ m/s.

Example 3 — Relative refractive index: Air-to-water: n₂₁ = 1.33 / 1.00 = 1.33 (light bends toward normal).

Dispersion and wavelength dependence

Most transparent materials have higher refractive index for shorter wavelengths (blue light). This phenomenon, dispersion, causes light splitting through prisms. For rough modeling, this calculator applies a small correction for glass-like materials if you provide wavelength (400–700 nm range).

Applications

• Optics design and lens calculations
• Fiber optics and waveguide design
• Understanding Snell’s law and total internal reflection
• Analyzing dispersion and chromatic aberration

Formula summary

• n = c / v
• v = c / n
• Relative index n₂₁ = n₂ / n₁

This calculator simplifies optical fundamentals while offering clarity and educational step-by-step insight.