Index of Refraction Calculator (n from speed, angles, critical angle or wavelength)

Understanding the index of refraction calculator — concept and principle

This calculator finds the refractive index of a material in four ways: from the speed of light in it, from a refraction measurement with Snell's law, from the critical angle of total internal reflection, or from the wavelength inside it. It then gives the light speed, critical angle into air, Brewster angle and wavelength inside. It is used in optics labs and to identify materials.

n is simply how many times slower light moves; 1.33 is close to water.

How it is calculated

n = c ÷ v, with c = 299,792.458 km/s

Snell's law: n = n₁ sin θ₁ ÷ sin θ₂

Critical angle: n = n₁ ÷ sin θ_c

Wavelength: n = λ₀ ÷ λ

Extra rows use air with n = 1.000293: critical angle sin θ_c = 1.000293 ÷ n; Brewster angle tan θ_B = n ÷ 1.000293.

The principle

Light slows down in matter because it interacts with the electrons of the material. The refractive index is the factor by which it slows. When light crosses a boundary at an angle, the part of the wavefront that enters first slows first, so the beam bends towards the normal; Snell's law describes this. The frequency stays the same across the boundary, so the slower speed shows up as a shorter wavelength. Going the other way, from dense to less dense, light beyond the critical angle cannot escape and is totally reflected.

Worked example

Default inputs: from speed, v = 225,000 km/s.

n = 299,792.458 ÷ 225,000 = 1.3324.
Light travels at 100 ÷ 1.3324 = 75.05% of c.
Critical angle into air = arcsin(1.000293 ÷ 1.3324) = 48.65°.
Brewster angle from air = arctan(1.3324 ÷ 1.000293) = 53.1°.
Wavelength inside for 589 nm light = 589 ÷ 1.3324 = 442.1 nm.

How to read the result

An index of 1.333 is the value for water at 589 nm, so the example describes water. Crown glass is about 1.52, and air is 1.000293. A higher index means slower light, stronger bending, a smaller critical angle and a larger Brewster angle. The index changes slightly with wavelength (dispersion), which is why prisms split white light.

Common mistakes

Measuring angles from the surface instead of from the normal.
Entering the critical angle measured in air instead of inside the denser material.
Comparing indices measured at different wavelengths.

Keep in mind: Indices depend on wavelength, temperature and composition. Use values measured at the wavelength you care about.

Frequently asked questions

What is the refractive index of water?

About 1.333 at 589 nm.

What is the Brewster angle?

The angle of incidence at which reflected light is completely polarised.

Can n be less than 1?

For visible light in ordinary transparent materials, no; special cases exist for X-rays and in some plasmas.

Sources: OpenStax, University Physics Volume 3 (2016), sections 1.1, 1.3, 1.4 and 1.7

Checked 9 Nov 2026. OpenStax, University Physics Volume 3 (2016): §1.1 “The Propagation of Light” (n = c/v; Table 1.1 “Index of Refraction in Various Media”: air 1.000293, water 1.333, crown glass 1.52); §1.7 “Polarization” (Brewster’s law tan θ_b = n₂/n₁); Chapter 1 Snell’s law and critical angle.

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