# Dielectric constant and index of refraction

1. Feb 24, 2005

### StatusX

I'm a little confused. My source says the dielectric constant for water is 80. Then I have the equation that gives the index of refraction as $n=\sqrt{\epsilon_r}$ (since it isn't very magnetic). But the index of refraction for water is 1.33. What am I missing?

2. Feb 24, 2005

### kirovman

They are both frequency dependent terms. However:

$$n(\omega) \equiv \sqrt{\epsilon(\omega)}$$

So your value are obviously not for the same frequency, you need to figure out which one is correct for the given frequency - I would guess refractive index implies the frequency is for visible light.

And your dielectric constant = 80 is relevant for a completeley different frequency ie not visible light.

3. Feb 24, 2005

### Claude Bile

Most quoted values for dielectric constant are for frequencies in the kHz, whereas visible light is hundreds of THz, so don't be surprised if there is a disrepancy. Refractive index values are measured at a standard optical frequency (Sodium D line perhaps, I'm not too sure).

What value you use obviously depends on what you are trying to solve.

Claude.

4. Feb 24, 2005

### Creator

Also varies with temperature.
DC = 80 corresponds to 80*F.(using radio frequency, Mhz). At 212*F, dielectric constant is ~53 for water.