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What is the Refractive Index?

Important Formula

Formula: Light Propagation in Medium

$$c_{\text m} ~=~ \frac{c}{n}$$ $$c_{\text m} ~=~ \frac{c}{n}$$ $$n ~=~ \frac{c}{c_{\text m}}$$ $$c ~=~ n \, c_{\text m}$$

Rearrange formula

What do the formula symbols mean?

Speed of light in medium

$$ c_{\text m} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Speed of light in medium is the speed at which light propagates for example in air, water or glass. Since the refractive index is $ n \ge 1 $, the speed of light in the medium is smaller than in vacuum.

Refractive Index

$$ n $$ Unit $$ - $$

Refractive index is characteristic of a transparent medium through which the light is transmitted. Vacuum has refractive index $ n = 1 $. Air has approximate value of $ n = 1.0003 $. Water $ n = 1.33 $. Quartz glass $ n = 1.46 $.

Refractive index is not always constant, but can depend, for example, on the frequency of the light used; but also on light intensity, light polarization and angle of incidence. In general, the refractive index is complex-valued, where the imaginary part of the refractive index, describes light absorption. The imaginary part can be neglected only for transparent media, because transparent media let the light pass without absorbing it.

Vacuum light speed

$$ c $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum: $$ c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} } $$

The refractive index $n$ is a dimensionless quantity describing the ratio of the speed of light $c$ in vacuum to the speed of light $c_{\text m}$ in a medium:

$$ \begin{align} n ~=~ \frac{c}{ c_{\text m} } \end{align} $$

Here the speed of light in vacuum is a physical constant with the value $ c = 3 \cdot 10^8 \, \frac{\mathrm m}{\mathrm s} $.

Different velocities of light in vacuum and in a medium.

So, to determine the refractive index, we have to send the light from the vacuum into a transparent medium (e.g. water, glass) and measure the speed of light in the medium. From the ratio 1 we can calculate the refractive index.

The refractive index $n$ is larger the slower the light propagates in the medium.
The refractive index $n$ is smaller the faster the light propagates in the medium. Since the vacuum light speed is the maximum possible speed in the universe, the refractive index cannot become smaller than $n=1$.

The term " refractive index" comes from the concept of light refraction. When a beam of light from a vacuum enters a medium at an angle, it is deflected (refracted) in the medium.

The refractive index depends on many factors, such as the wavelength of the light, the transparency of the medium, the temperature of the medium, and so on. The following table lists some examples of refractive indices.

Table : Approximate refractive indices of different media with light wavelength 590 nanometers
Medium	Refractive index
Vacuum	1
Air	1
Water (20 degrees)	1.3
Window glass	1.5
Diamond	2.4