Do the Relative Permittivity and Refractive Index of Water Match Up?

[DaMasta345]

Many textbooks and online sources give the relative permittivity of water as about 80 and the refractive index as 1.33. If you use the definition of refractive index to find the speed of light in water, you will find v = c/n ~ 2.56e8 m/s. However, if you use the equation to find the speed of light in a medium, c = 1/sqrt(permittivity*permeability), you will find c ~ 0.335e8 m/s, which is off from the former calculation by a factor of 10. I tried to find the complex permittivity of water, but because the conductivity of water is relatively low, the imaginary portion of the permittivity will be small, and thus I am lost. Did I do something wrong or is there another explanation to this discrepancy?

 

[nasu]

Both permitivity and index of refraction are functions of frequency.
The refractive index of 1.33 is measured at frequencies corresponding to visible light range.
The value of 80 for permitivity is measured in DC regime or very low frequency.
You need to use the values measured at the same frequency for that formula to hold.