# Calculating phase velocity in a material

1. Nov 30, 2011

### Julle

Calculating wavelength in a media

Hi

Trying to get how to calculate the wavelength of an electromagnetic wave in a media and I am getting confused about the permittivity.

I know the formula:

vphase = c/(sqrt(εrr))

where vphase is the phase velocity.
c is the speed of light in a vacuum.
εr is the relative permittivity.
μr is the relative permability.

Then to get the wavelength we do like this:

λ = vphase/f

where λ is the wavelength and f the frequency.

This is all well and good, but isn't there a real and imaginary part to the permittivity? Is only the real part used or is the entire complex number used in which case you end up with a complex distance??

Last edited: Nov 30, 2011
2. Nov 30, 2011

### Staff: Mentor

Re: Calculating wavelength in a media

I've never heard of it being anything but real? Can you cite something that causes you to think it is a complex number?

3. Nov 30, 2011

### Julle

Re: Calculating wavelength in a media

http://www.random-science-tools.com/electronics/water_dielectric.htm

One of many but shows the principle nicely.

The dielectric constant is for most (all?) dielectric materials frequency dependant and is often written as εr=ε'-iε''

where ε' is the real part and is related to the stored energy inside the medium
ε'' is the imaginary part and related to the loss inside the medium

https://en.wikipedia.org/wiki/Permittivity