Index of Refraction Calculator

The index of refraction (n) measures how much slower light travels through a given medium compared to its speed in a vacuum. It is the ratio of the speed of light in vacuum (c = 299,792,458 m/s) to the speed of light in the medium (v), expressed as n = c/v. A higher refractive index means light slows down more in that medium.

The refractive index of water at 20°C is approximately 1.333. This means light travels about 1.333 times slower in water than in a vacuum, with a speed of roughly 225,000 km/s in water. The exact value varies slightly with temperature and wavelength of light.

The refractive index of glass depends on its type. Crown glass typically has a refractive index of about 1.52, while flint glass ranges from about 1.60 to 1.70. Diamond, often used in optical instruments, has one of the highest refractive indices at about 2.417.

The refractive index is a dimensionless quantity — it has no SI unit. Since it is defined as the ratio of two speeds (speed of light in vacuum divided by speed of light in the medium), the units cancel out, leaving a pure number always greater than or equal to 1.

Rearrange the formula n = c/v to get v = c/n. Simply divide the speed of light in vacuum (299,792,458 m/s) by the refractive index of the medium. For example, in water (n = 1.333), the speed of light is 299,792,458 / 1.333 ≈ 224,900 km/s.

Snell's Law describes how light bends when passing from one medium to another: n₁ × sin(θ₁) = n₂ × sin(θ₂), where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal. The greater the difference in refractive indices, the more the light bends.

The critical angle is the angle of incidence above which total internal reflection occurs, meaning no light passes into the second medium. It exists only when light travels from a denser medium (higher n) to a less dense one (lower n). The critical angle θc is calculated as θc = arcsin(n₂/n₁).

Dissolving sugar in water increases its refractive index above the pure water value of 1.333. Higher sugar concentrations cause a greater increase in refractive index. This principle is used in refractometers to measure the sugar content (Brix) of solutions in food and beverage industries.