Refractive index

The refractive index of a particular material at a particular frequency is the factor by which electromagnetic radiation of that frequency is slowed down (relative to vacuum) when it travels inside the material.

The speed of all electromagnetic radiation in vacuum is the same, approximately 3*10⁸ meters per second, and is denoted by c. So if v is the [phase velocity]? of radiation of a specific frequency in a specific material, then the refractive index is given by

n = v/c.

This number is typically bigger than one: the denser the material, the more the light is slowed down. However for x-ray radiation of high frequencies, n will actually be smaller than one. This does not contradict the theory of relativity, which holds that no information carrying signal can ever propagate faster than c, because the [phase velocity]? is not the same as the [signal velocity]?.

The signal velocity is the velocity with which the leading edge of a beam of light travels; it cannot exceed c. For the definition of the refractive index, the phase velocity is used; it is the velocity with which peaks of the wave travel and it may be bigger than c.

If the refractive indices of two materials are known for a given frequency, then one can compute the angle by which radiation of that frequency will be refracted as it moves from the first into the second material (see refraction).

As mentioned above, the refractive index varies with frequency (except in vacuum, where all frequencies travel at the same speed, c). This effect, known as dispersion, lets a prism divide white light into its constituent spectral colors, explains rainbows, and is the cause of [chromatic aberration]? in lenses.

Some representative refractive indices of yellow light (wavelength 560 nm) and x-rays (wavelength 0.1 nm):

  Material      n (yellow)   n (x-ray)
    air          1.0002        ????
    water        1.333         ????
    glass        1.5           ????
    diamond      2.4           ????

When light enters a diamond, the high refractive index causes it to suffer multiple total internal reflections, which is the reason for the brilliance of these gemstones.

/talk