Relative Permittivity and Refractive Index

[iLIKEstuff]

in relating the index of refraction to the relative permittivity (dielectric constant/function). it is known that $$n = \sqrt{\epsilon_r}$$ for optical frequencies (i.e. $$\mu_r=1$$.

now this website
http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/diel.html#c1

gives the relative permittivity of water as 80.4 i.e. $$\epsilon_r = 80.4$$
but we also know that the index of refraction of water is 1.33.

so it should be $$n = \sqrt{\epsilon_r} = \sqrt{80.4} = 8.9666$$ ? am i missing something here?

i want to use the relative permittivity in an equation to calculate the electrostatic approximation of the scattering/absorption efficiencies of small spherical particles.

should i be solving for relative permittivity from the index of refraction? i.e. $${n}^{2} = {(\sqrt{\epsilon_r})}^{2} \Rightarrow \epsilon_r={1.33}^{2}=1.7689$$

what value should i use for the relative permittivity in this equation?

thanks guys.

 

[mpolyanskiy]

Permittivity is a function of wavelength (frequency). 80.4 value is valid for microwave diapason, not for optical one.

For optical frequencies you should calculate permittivity from refractive index, i.e. $$\epsilon_r = n^2$$

To find accurate value of n at a particular wavelength in optical diapason use, for example, http://refractiveindex.info/"

 

[astrokreng]

Your understanding is correct. The relationship between the index of refraction and the relative permittivity is given by n = \sqrt{\epsilon_r}. In the case of water, the relative permittivity is 80.4 and the index of refraction is 1.33. This means that n = \sqrt{80.4} = 8.9666.

In your equation for calculating the electrostatic approximation of scattering/absorption efficiencies, you should use the relative permittivity value of 80.4. This is because the equation is dependent on the dielectric constant, which is represented by the relative permittivity.

You can also solve for the relative permittivity from the index of refraction, as you have shown in your calculation. This can be useful if you have the index of refraction and want to find the corresponding relative permittivity.

In summary, the value of relative permittivity should be used in your equations, not the index of refraction. The index of refraction is related to the relative permittivity through the square root relationship n = \sqrt{\epsilon_r}.