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Does all frequency of light travel with the same speed in a particular material like glass?

Since by cauchy's relation refractive index change with wavelength which implies the speed also changes.

But as derived from maxwells equation, the speed of light should only depent on medium through which it travel and not on its frequency or wavelength. V=1/sqrt(epsilon*mu)

Does different colours have different speed in a particular medium?

Qmechanic
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user40428
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1 Answers1

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Yes. Different colors of visible light have different speeds in a particular medium.

The index of refraction of a medium is defined as the ratio of $c$, the speed of light in vacuum, to $v$ the speed of light in the medium; \begin{align} n = \frac{c}{v} \end{align} Therefore, as you essentially point out, if the index depends on wavelength, then so does the speed. This is precisely why, for example, a prism splits white light into its component colors.

See also dispersion relation.

joshphysics
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  • but what about maxwells equation.They imply all electromagnetic waves travel with same speed – user40428 Feb 19 '14 at 06:21
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    @user40428 Maxwell's equations predict that in a linear medium with permittivity $\epsilon$ and permeability $\mu$, the speed of light in the medium will be $v = 1/\sqrt{\epsilon\mu}$. When the medium is dispersive, the permittivity depends on wavelength, so Maxwell's equations tell us that the speed of light in the medium also depends on wavelength. – joshphysics Feb 19 '14 at 06:29