Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Index of refraction = sqrt dielectric constant

  1. May 8, 2008 #1


    User Avatar
    Gold Member

    Can someone explain in terms of electric fields how the index of refraction squared = the dielectric constant of the material ?
  2. jcsd
  3. May 9, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The index of refraction is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. If one solves the wave equation for the electric (or magnetic) wave in a dielectric medium it turns out that the speed of propagation is,

    [tex]v = \frac{1}{\sqrt{\varepsilon_0\mu_0\varepsilon\mu}}[/tex]

    And the speed of light in vacuum is,

    [tex]c = \frac{1}{\sqrt{\varepsilon_0\mu_0}}[/tex]

    Hence, taking the ratio of the two yields,

    [tex]n = \frac{c}{v} = \sqrt{\varepsilon\mu}[/tex]

    Note that [itex]\mu\approx1[/itex] for most materials with light in the optical range.
    Last edited: May 9, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook