Index of refraction = sqrt dielectric constant

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SUMMARY

The index of refraction (n) of a material is definitively expressed as the square root of the product of its dielectric constant (ε) and magnetic permeability (μ). The relationship is derived from the wave equation for electric waves in a dielectric medium, where the speed of light in a vacuum (c) is compared to the speed of propagation (v) in the medium. The formula n = c/v simplifies to n = √(εμ), with μ approximated as 1 for most optical materials, confirming that n² = ε.

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morrobay
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Can someone explain in terms of electric fields how the index of refraction squared = the dielectric constant of the material ?
 
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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,

v = \frac{1}{\sqrt{\varepsilon_0\mu_0\varepsilon\mu}}

And the speed of light in vacuum is,

c = \frac{1}{\sqrt{\varepsilon_0\mu_0}}

Hence, taking the ratio of the two yields,

n = \frac{c}{v} = \sqrt{\varepsilon\mu}

Note that \mu\approx1 for most materials with light in the optical range.
 
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