Many materials have well-characterized refractive indices, but these indices depend strongly on the frequency of light. Therefore, any numeric value for the index is meaningless unless the associated frequency is specified.

There are also weaker dependencies on temperature, pressure/stress, and so forth, as well as on precise material compositions. For many materials and typical conditions, however, these variations are at the percent level or less. It is therefore especially important to cite the source for an index measurement, if precision is required.

In general, an index of refraction is a complex number with both a real and an imaginary part, where the latter indicates the strength of absorption loss at a particular wavelength-thus, the imaginary part is sometimes called the extinction coefficient k. Such losses become particularly significant-for example, in metals at short wavelengths (such as visible light)-and must be included in any description of the refractive index.

Dispersion and absorption

In real materials, the polarization does not respond instantaneously to an applied field. This causes dielectric loss, which can be expressed by a permittivity that is both complex and frequency dependent. Real materials are not perfect insulators either, meaning they have non-zero Direct Current (DC) conductivity. Taking both aspects into consideration, we can define a complex index of refraction:

Here, n is the refractive index indicating the phase velocity, while κ is called the extinction coefficient, which indicates the amount of absorption loss when the electromagnetic wave propagates through the material. Both n and κ are dependent on the frequency.

The effect that n varies with frequency (except in vacuum, where all frequencies travel at the same speed c) is known as dispersion, and it is what causes a prism to divide white light into its constituent spectral colors, which is how rainbows are formed in rain or mists. Dispersion is also the cause of chromatic aberration in lenses.

Since the refractive index of a material varies with the frequency (and thus wavelength) of light, it is usual to specify the corresponding vacuum wavelength at which the refractive index is measured. Typically, this is done at various well-defined spectral emission lines; for example, nD is the refractive index at the Fraunhofer "D" line, the centre of the yellow sodium double emission at 589.29 nm wavelength.

The Sellmeier equation is an empirical formula that works well in describing dispersion, and Sellmeier coefficients are often quoted instead of the refractive index in tables. For some representative refractive indices at different wavelengths, see list of indices of refraction.

As shown above, dielectric loss and non-zero DC conductivity in materials cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low frequencies the dielectric loss is also negligible, resulting in almost no absorption (κ ≈ 0). However, at higher frequencies (such as visible light), dielectric loss may increase absorption significantly, reducing the material's transparency to these frequencies.

The real and imaginary parts of the complex refractive index are related through use of the Kramers-Kronig relations. For example, one can determine a material's full complex refractive index as a function of wavelength from an absorption spectrum of the material.


A calcite crystal laid upon a paper with some letters showing birefringence.

The refractive index of certain media may be different depending on the polarization and direction of propagation of the light through the medium. This is known as birefringence and is described by the field of crystal optics.


The strong electric field of high intensity light (such as output of a laser) may cause a medium's refractive index to vary as the light passes through it, giving rise to nonlinear optics. If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self-focusing and self phase modulation. If the index varies linearly with the field (which is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect.


A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.

If the refractive index of a medium is not constant, but varies gradually with position, the material is known as a gradient-index medium and is described by gradient index optics. Light traveling through such a medium can be bent or focussed, and this effect can be exploited to produce lenses, some optical fibers and other devices. Some common mirages are caused by a spatially varying refractive index of air.


The refractive index of a material is the most important property of any optical system that uses the property of refraction. It is used to calculate the focusing power of lenses and the dispersive power of prisms.

Since refractive index is a fundamental physical property of a substance, it is often used to identify a particular substance, confirm its purity, or measure its concentration. Refractive index is used to measure solids (glasses and gemstones), liquids, and gases. Most commonly, it is used to measure the concentration of a solute in an aqueous solution. A refractometer is the instrument used to measure refractive index. For a solution of sugar, the refractive index can be used to determine the sugar content.

In medicine, particularly ophthalmology and optometry, the technique of refractometry utilizes the property of refraction for administering eye tests. This is a clinical test in which a phoropter is used to determine the eye's refractive error and, based on that, the best corrective lenses to be prescribed. A series of test lenses in graded optical powers or focal lengths are presented, to determine which ones provide the sharpest, clearest vision.

Alternative meaning: Refraction in metallurgy

In metallurgy, the term refraction has another meaning. It is a property of metals that indicates their ability to withstand heat. Metals with a high degree of refraction are referred to as refractory. These metals have high melting points, derived from the strong interatomic forces that are involved in metal bonds. Large quantities of energy are required to overcome these forces.

Examples of refractory metals include molybdenum, niobium, tungsten, and tantalum. Hafnium carbide is the most refractory binary compound known, with a melting point of 3,890 degrees C.12

See also

  • Birefringence
  • Light
  • Reflection (physics)
  • Sound


  • Fishbane, Paul M., et al. 2005. Physics for Scientists and Engineers, 3rd ed. Upper Saddle River, NJ: Pearson Education. ISBN 0131418815.
  • Hecht, Jeff. 2006. Red Light Debut for Exotic 'Metamaterial.' News Service. 13:38. Retrieved March 28, 2007.
  • Henderson, Tom. 2004. Refraction and the Ray Model of Light. The Physics Classroom. Retrieved February 20, 2007.
  • Ward, David W., Keith A. Nelson, and Kevin J. Webb. 2005. On the Physical Origins of the Negative Index of Refraction. New Journal of Physics 7:213. Retrieved March 28, 2007.

External links

All links retrieved July 27, 2019.

  • Refraction through a Prism. (Java simulation.)
  • Index of Refraction - Eric Weisstein's World of Physics.
  • Index of Refraction - Hyperphysics. (List of refractive indices.)