# Optics: refractive index and dielectric constant

1. Dec 18, 2005

### ivas

Dear all,
i am a bit confused with a very simple equation connecting refractive index of water and its dielectric constant for visible range of wavelengths and room temperature. :grumpy:

i hope, You can help me

as we know, the refractive index 'n' can be defined as

n=sqrt(epsilon*mu), (http://en.wikipedia.org/wiki/Refractive_index)

where 'epsilon' is material's dielectric constant (or material's relative permittivity) and 'mu' is its relative permeability.

for water we have:
mu is almost 1, epsilon=80 (http://en.wikipedia.org/wiki/Dielectric_constant)

it means that (using the equation above) the refractive index of water is n=sqrt(80)=8.94, but the measured refractive index of water at room temperature is about 1.33 (http://www.ps.missouri.edu/rickspage/refract/refraction.html, http://www.cargille.com/certwater.shtml) [Broken].

Thus, refractive index computed from the equation is not the same and not near to its experimental quantity.

Where is my fault?
Thanks

Last edited by a moderator: May 2, 2017
2. Dec 18, 2005

### Staff: Mentor

The dielectric constant depends strongly on the frequency of the applied field. While the dielectric constant of water is 80 for a static field, it is much lower for optical frequencies (around 1.78, according to one reference I found).

3. Dec 18, 2005

### ivas

Thanks,
i agree,

4. Dec 25, 2005

### wangasu

For crystals, the dielectric constant does generally not change too much with measurement frequency (if temperatrue is not high), and thus the equation still gets along with the low frequency values of permittivity. But for liquids, molecular movements (or dipole reorientation) have a dominant (say to be excess) contribution to static permittivity. In this case, only the high frequency value of permittivity follows the equation.

Last edited: Dec 26, 2005
5. Nov 12, 2009

### SHeck

I was wondering if you could give me a link to that reference.

I am also looking for values for the dielectric constant for water and silica (SiO2) in the visible. Any suggestions where I could find them?

Lastly, a little aside...I am also struggling to find the refractive index of SF6 gas at std T and P, or at RT (~20C-30C), any suggestions?

Thank you in advance

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