Calculate Refractive Index

Online calculator and formulas for light speed in media

Refractive Index Calculator (JavaScript)

Core formula

Refractive index is given by n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium.

m/s
Result

Example calculations

Example 1: Refractive index of water

Given: v = 225,000,000 m/s

\[n=\frac{c}{v}=\frac{299792458}{225000000}=1.33\]

Result: n ≈ 1.33

Example 2: Speed in glass

Given: n = 1.50

\[v=\frac{c}{n}=\frac{299792458}{1.50}=199861639\,m/s\]

Result: v ≈ 199,861,639 m/s

Example 3: Medium comparison

The larger n is, the slower light propagates in the medium.

Typical: Air ~1.00, water ~1.33, glass ~1.5.

Refractive index formulas

Refractive index describes the ratio between the speed of light in vacuum and in a medium.

Refractive index
\[n=\frac{c}{v}\]
Velocity
\[v=\frac{c}{n}\]
Vacuum
\[c=299792458\,m/s\]
Valid for
\[n\ge 1\]

Description

What is the Refractive Index?

The refractive index (also called index of refraction or refractive number) is a dimensionless physical quantity that describes how much light is slowed down when passing through a material. Every transparent material has a characteristic refractive index. The higher this value, the slower light travels through the material and the more strongly light is refracted when entering the material.

Basic Formula for Refractive Index

The refractive index is defined as the ratio of the speed of light in vacuum c to the speed of light in a medium v:

\[n = \frac{c}{v}\]
  • n – refractive index (dimensionless)
  • c – speed of light in vacuum ≈ 299,792,458 m/s
  • v – speed of light in the medium in m/s

The refractive index is always greater than or equal to 1, since light never travels faster than it does in vacuum.

Typical Refractive Indices of Various Substances
Material Refractive Index n Speed of Light v
Vacuum 1.00 299,792,458 m/s
Air (at 0°C) 1.000293 ≈ 299,700,000 m/s
Water (at 20°C) 1.33 ≈ 225,000,000 m/s
Ethanol 1.36 ≈ 220,000,000 m/s
Glass (crown glass) 1.52 ≈ 197,000,000 m/s
Glass (flint glass) 1.65 ≈ 182,000,000 m/s
Diamond 2.42 ≈ 124,000,000 m/s
Connection to Light Refraction

The refractive index is closely related to Snell's Law of Refraction, which describes how light is bent at the interface between two materials:

\[n_1 \sin(θ_1) = n_2 \sin(θ_2)\]

A material with a higher refractive index causes stronger light refraction. This explains why water has a higher refractive index than air and why objects in water appear distorted or shifted.

Practical Applications
  • Optical instruments: Lens systems in microscopes, cameras, and telescopes utilize different refractive indices
  • Fiber optics: Optical fibers rely on differences in refractive index for light confinement
  • Eyeglasses: High-refractive-index glasses allow for thinner and lighter lenses
  • Liquid analysis: Refractometers determine substance concentrations by measuring refractive index
  • Coatings: Anti-reflective coatings deliberately use different refractive indices
Note
The refractive index depends on the wavelength of light (dispersion). This is why white light is split into its spectrum colors when passing through a prism. Therefore, we often refer to the refractive index at a specific wavelength (e.g., at the sodium D-line).
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