<P> Another reason for the speed of light to vary with its frequency would be the failure of special relativity to apply to arbitrarily small scales, as predicted by some proposed theories of quantum gravity . In 2009, the observation of the spectrum of gamma - ray burst GRB 090510 did not find any difference in the speeds of photons of different energies, confirming that Lorentz invariance is verified at least down to the scale of the Planck length (l = √ ħ G / c ≈ 6965161630000000000 ♠ 1.6163 × 10 m) divided by 1.2 . </P> <P> In a medium, light usually does not propagate at a speed equal to c; further, different types of light wave will travel at different speeds . The speed at which the individual crests and troughs of a plane wave (a wave filling the whole space, with only one frequency) propagate is called the phase velocity v. An actual physical signal with a finite extent (a pulse of light) travels at a different speed . The largest part of the pulse travels at the group velocity v, and its earliest part travels at the front velocity v . </P> <P> The phase velocity is important in determining how a light wave travels through a material or from one material to another . It is often represented in terms of a refractive index . The refractive index of a material is defined as the ratio of c to the phase velocity v in the material: larger indices of refraction indicate lower speeds . The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material - dependent constant . The refractive index of air is approximately 1.0003 . Denser media, such as water, glass, and diamond, have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light . In exotic materials like Bose--Einstein condensates near absolute zero, the effective speed of light may be only a few metres per second . However, this represents absorption and re-radiation delay between atoms, as do all slower - than - c speeds in material substances . As an extreme example of light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a Bose--Einstein condensate of the element rubidium, one team at Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other at the Harvard--Smithsonian Center for Astrophysics, also in Cambridge . However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse . During the time it had "stopped," it had ceased to be light . This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light . </P> <P> In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than c . In other materials, it is possible for the refractive index to become smaller than 1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative . The requirement that causality is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient, are linked by the Kramers--Kronig relations . In practical terms, this means that in a material with refractive index less than 1, the absorption of the wave is so quick that no signal can be sent faster than c . </P>

Velocity of light is minimum in which medium
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