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

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SUMMARY

The discussion centers on the discrepancy between the relative permittivity of water, cited as approximately 80, and its refractive index, measured at 1.33. Calculating the speed of light in water using the refractive index yields approximately 2.56e8 m/s, while using the permittivity and permeability results in a significantly lower speed of 0.335e8 m/s. This inconsistency arises because the refractive index is determined at visible light frequencies, whereas the permittivity value is measured in the DC regime or at very low frequencies. To resolve this discrepancy, it is essential to use values measured at the same frequency.

PREREQUISITES
  • Understanding of refractive index and its calculation
  • Knowledge of relative permittivity and permeability
  • Familiarity with electromagnetic wave propagation
  • Basic concepts of frequency dependence in materials
NEXT STEPS
  • Research the frequency dependence of permittivity and refractive index in various materials
  • Learn about complex permittivity and its implications in low conductivity materials
  • Explore the relationship between electromagnetic wave speed and material properties
  • Investigate measurement techniques for permittivity and refractive index at different frequencies
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Physicists, materials scientists, and engineers involved in optics, electromagnetic theory, and material characterization will benefit from this discussion.

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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?
 
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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.
 
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