Refractive index

In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, $n 1 sin θ 1 = n 2 sin θ 2$ , where $θ 1$ and $θ 2$ are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices $n 1$ and $n 2$ . The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle.^[1]

The refractive index, $n$ , can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is $v = c/ n$ , and similarly the wavelength in that medium is $λ = λ 0 / n$ , where $λ 0$ is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the frequency ( $f = v / λ$ ) of the wave is not affected by the refractive index.

The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion. This effect can be observed in prisms and rainbows, and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index.^[2] The imaginary part then handles the attenuation, while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Consequently, refractive indices for materials reported using a single value for $n$ must specify the wavelength used in the measurement.

The concept of refractive index applies across the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case, the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.^[3]

For lenses (such as eye glasses), a lens made from a high refractive index material will be thinner, and hence lighter, than a conventional lens with a lower refractive index. Such lenses are generally more expensive to manufacture than conventional ones.

^ Hecht, Eugene (2002). Optics. Addison-Wesley. ISBN 978-0-321-18878-6.
^ Attwood, David (1999). Soft X-rays and extreme ultraviolet radiation: principles and applications. Cambridge University Press. p. 60. ISBN 978-0-521-02997-1.
^ Kinsler, Lawrence E. (2000). Fundamentals of Acoustics. John Wiley. p. 136. ISBN 978-0-471-84789-2.

[Hecht-1] Hecht, Eugene (2002). Optics. Addison-Wesley. ISBN 978-0-321-18878-6.

[Attwood-2] Attwood, David (1999). Soft X-rays and extreme ultraviolet radiation: principles and applications. Cambridge University Press. p. 60. ISBN 978-0-521-02997-1.

[Kinsler-3] Kinsler, Lawrence E. (2000). Fundamentals of Acoustics. John Wiley. p. 136. ISBN 978-0-471-84789-2.

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