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MasterMath

Refractive Index Calculator

The refractive index is how much light slows in a medium, and it is what makes light bend when it crosses a boundary.

Result

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How this was worked out

    The formula

    n = c / v

    SymbolQuantityUnit
    nRefractive index
    vSpeed in the mediumm/s
    θ₁Angle of incidence°
    θ₂Angle of refraction°

    What it means

    Light travels slower in matter than in a vacuum, and the refractive index is the ratio of the two speeds. That change of speed at a boundary is exactly what bends the ray, which is Snell's law.

    How to work it out by hand

    1. Divide the speed of light in a vacuum by the speed in the medium
    2. The result has no units
    3. It is always at least 1 for ordinary materials

    What is worth knowing

    Water's index of 1.33 is why a straw looks bent in a glass and why a pool is shallower than it appears. Glass is around 1.5 and diamond 2.42, and diamond's exceptionally high value is what gives it its brilliance: it produces total internal reflection at only 24°, so light entering the top bounces around inside before coming back out. The index also varies slightly with wavelength, which is dispersion, and that is the whole reason a prism separates white light into colours.

    Frequently asked questions

    Why does light bend when it enters water?

    Because it slows down. The change of speed at an angle redirects the ray, which is Snell's law.

    What is total internal reflection?

    When light hits a boundary beyond a critical angle and reflects entirely instead of passing through. It is how optical fibres work.

    Why does a diamond sparkle?

    Its refractive index of 2.42 gives a critical angle of just 24°, so light bounces around inside before escaping.

    Can the refractive index be less than 1?

    Not for the speed that carries information. Some engineered metamaterials show unusual behaviour, but ordinary materials are always above 1.