Index Of Refraction Calculator

What the index of refraction calculator does

The refractive index of a material measures how much it slows light down. This calculator finds it from the speed of light in the material, and it can also compare two materials by computing the relative index between them. Presets cover common media from air and water to glass and diamond.

Below is what the refractive index is, the equation behind it, how the absolute and relative versions differ, and a worked example.

How to use it

1. Choose the mode: absolute index for a single material, or relative index to compare two.
2. Enter the speed of light in the material, or pick a preset medium to fill it in.
3. Press Calculate for the refractive index, or Reset to clear it.

What the refractive index is

The refractive index of a material is the number that tells you how much slower light travels inside it compared with travelling through empty space. Light moves fastest in a vacuum, and in any material it is slowed, by a little in air and by a lot in dense, transparent solids. The refractive index captures that slowing in a single figure: a value of 1 means light travels at its full vacuum speed, while a value of 1.5 means light travels two-thirds as fast.

Because the bending of light at a surface comes directly from this change in speed, the refractive index is the key property behind all of refraction. It is what determines how sharply a lens focuses, how much a prism spreads white light into colours, and how a diamond bends and traps light to sparkle. Every transparent material has its own refractive index, and knowing it is the starting point for any optical design. This calculator computes it from the speed of light in the material.

The equation it uses

The absolute refractive index is the speed of light in vacuum divided by its speed in the material:

n = c ÷ v

Here n is the refractive index, c is the speed of light in vacuum, and v is the speed of light in the material. Since light is always slower in a material than in vacuum, v is smaller than c and the index is always greater than 1. The more a material slows light, the smaller v becomes and the larger the index. The calculator divides the fixed vacuum speed by the speed you enter to give the index.

Absolute and relative index

There are two ways to express a refractive index, and the calculator handles both. The absolute index compares the speed of light in a material with its speed in vacuum, and it is the value usually quoted for a material on its own. The relative index, by contrast, compares the speeds of light in two materials directly, telling you how light behaves when passing specifically from one into the other.

The relative index of one medium with respect to another is simply the ratio of the light speeds in the two, which also equals the ratio of their absolute indices. It is the quantity that actually governs refraction at the boundary between those two materials, since what matters there is the change in speed from one to the other rather than from vacuum. The calculator's relative mode works this out for any pair of media, which is exactly what you need when applying Snell's law to a real interface like water against glass.

Why a higher index bends light more

A higher refractive index means light is slowed more, and the more light's speed changes at a boundary, the more sharply it bends. This is why the refractive index is such a useful single number: it predicts not just how fast light goes in a material but how strongly that material will refract a ray entering it. Diamond, with an index of about 2.42, bends light far more than water, with an index of about 1.33, which is part of why cut diamonds are so dazzling.

The index also varies slightly with the colour of the light, being a touch higher for blue than for red in most materials. That small difference is what splits white light into a spectrum when it passes through a prism or a raindrop, since each colour bends by a slightly different amount. So the refractive index not only governs how much light bends but, through its gentle dependence on colour, gives us rainbows. The calculator reports the index that drives all of this.

Units and precision

The calculator takes the speed of light in the material in your choice of units, including a fraction of the speed of light, with presets carrying the standard speeds for vacuum, air, water, ethanol, ice, acrylic, glass, and diamond. The refractive index it returns is a plain number with no units, since it is a ratio of two speeds. The calculation is an exact application of the definition, and results carry several significant figures.

A worked example

Light travels through water at about 224,900,569 metres per second, slower than its vacuum speed of 299,792,458 metres per second.

The refractive index of water is n = c ÷ v = 299,792,458 ÷ 224,900,569 ≈ 1.333, the familiar value. For comparison, diamond slows light to about 124 million metres per second, giving it a refractive index of about 2.42, which is why diamond bends and traps light so much more strongly than water does.

Questions people ask

How do you calculate the refractive index?

Divide the speed of light in vacuum by its speed in the material, n = c/v. Since light is always slower in a material, the index is always greater than 1.

What does a refractive index of 1.5 mean?

That light travels 1.5 times slower in the material than in vacuum, at two-thirds of its vacuum speed. Window glass has an index near this value.

What is the relative refractive index?

The ratio of the speeds of light in two materials, which governs how light refracts passing from one into the other. It equals the ratio of their absolute indices.

Why does a higher index bend light more?

Because a higher index means a bigger change in light's speed at the boundary, and the greater the speed change, the sharper the bend. Diamond, with a high index, bends light far more than water.

References

A quick note on where the physics comes from. The refractive index as the ratio of light speeds is standard optics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics, which also tabulates index values for many materials. The speed of light follows the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 3, Section 1.4, Refraction. https://openstax.org/books/university-physics-volume-3/pages/1-4-refraction
2. HyperPhysics, Index of Refraction. http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, Speed of light in vacuum. https://physics.nist.gov/cgi-bin/cuu/Value?c