Index of refraction

The index of refraction comes from the phenomenon of Réfraction which indicates the change of management of the Lumière to the passage of a medium to another. The concept of index was initially introduced empirically like coefficient into the Lois of Snell-Descartes.

The index like characteristic of propagation

The index of refraction of a medium determined for some Radiation Monochromatique characterizes the propagation velocity of this radiation in this medium, v being the propagation velocity of the radiation considered in the studied medium.

More precisely, the index of refraction of the medium has compared to the medium B is the report/ratio speeds $v\_B/v\_A$, $v\_A$ and $v\_B$ being speeds of the same simple radiation in the mediums have and B. If the medium B is the vacuum, speed $v\_B$ is equal to the constant C   =  299  792  458  m/s (Celerity of the light), and the index of refraction are called absolute index: $n\; =\; \backslash \; frac\; \{C\}\; \{v\}$

In the model of the electromagnetic Wave, celerity in the Vide is connected to the electromagnetic properties of the vacuum (ɛ₀μ₀c ² = 1) and the index is thus related to the permittivity and permeability of material: ɛ_r, μ_r.

Foot-note Bucket: in all that precedes, the formulations relating to speed in the medium, implies the existence a single speed and thus that the material is homogeneous and isotropic.

Dependence of the index according to the wavelength

The value of the index generally depends on the Wavelength of the luminous ray used.

The first consequence is the effect on the refraction: the angle of refraction is not the same one for various “colors”. This explains the decomposition of the light by a prism or water drops (Arc-en-ciel).

The indexes of refraction must thus refer to a precise monochromatic radiation: the line D of helium (wavelength 587,6 Nm), near to the medium of the visible spectrum, is frequently used like reference. One also uses the line D of sodium (wavelength 589 Nm). It thus should be paid attention since both tend to be represented by the index “$n\_D$”, but since the values two wavelengths are very close one of the other, the indices are generally equivalent in both cases, taking into account the district of the decimals and uncertainties related to the measuring instruments.

The variation of the index of refraction of a transparent medium in the visible spectrum is called Dispersion; it is characterized by the Nombre or scatter coefficient of Abbot:

$\backslash \; naked\; =\; \backslash \; frac\; \{n\_D\; -\; 1\}\; \{n\_F\; -\; n\_C\}$

F and C indicating two lines of hydrogen (wavelengths $\backslash \; lambda\_F$ = 486,1 Nm and $\backslash \; lambda\_C$ = 656,3 Nm)

For radiation D, the absolute index $n\_D$ of the Eau to 20°C is of 1,333; that of a ordinary Verre lies between 1,511 to 1,535.

Dependence of the index according to the conditions related to the medium

The index of a medium depends on the parameters which characterize the medium: temperature, pressure, density, etc

Thus, the index of the Air is equal to 1,000  292  6 under the normal conditions of temperature and pressure, but this index depends on the density on the air, and its continuous variation between layers of air of different temperature. This makes it possible to explain the Mirage S.

The constraints imposed on a transparent material modify its index. The consequence is generally the appearance of a birefringence related to the anisotropy which results from it. This is used to study certain mechanical structures.

Birefringence

The birefringent mediums have two indexes of refraction, called ordinary index and extraordinary index , which corresponds to radiations of different polarization S.

Multiple indices in crystalline materials

Certain materials do not have a constant index according to the direction of light propagation. It is the case of certain crystals known as crystals Anisotropes.

List indexes of refraction

References

• ¹ : BlenderArt n°7, free diffusion, by JDragonB - FLAHAUT Samuel

See too

• List of the indexes of refraction

• Laws of Snell-Descartes
• Refraction
• optical Diopter
• Way
• geometrical Principle of Fermat
• Optical

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