# Relationship between Refractive index and Inpedance

1. Nov 28, 2009

### Plutoniummatt

as described in the title, whats the relationship between these 2 quantities in a given material? ty

2. Nov 28, 2009

### wywong

Did you mean impedance?

Refractive index and impedance are unrelated properties. For example, some non-conductive liquids have higher refractive indexes than tap water (which is conductive) and some lower.

Wai Wong

3. Nov 28, 2009

### Bob S

Nice question. I have never thought about this before. The characteristic impedance of free space is Z0 = sqrt(u0/e0) = 377 ohms, where u0 and e0 are the permeability and permittivity of free space. So the characteristic impedance of a dielectric with index of refraction n is
Z= sqrt(u0/n2e0) = Z0/n.
Bob S

4. Nov 28, 2009

### Plutoniummatt

Thanks Bob,

Im trying to work out the impedance of a typical metal.

and I've narrowed it down to (1-i)a

with a = sqrt ( wuu0 / 2(sigma) ).

where w = angular freq of the incident EM Radiation
u = relative permeability
u0 = free space permeability
sigma = conductivity

if I now use Z = Z0/n to find out refractive index, i can get wave vector k which i can substitute back into the EM radiation equation (assuming plane wave) and I am 99% sure that Z does indeed = Z0/n as you said.

Exp i(kz - wt)

to see how the wave behaves once inside the material. However if I do this. I get something that disagrees with whats in the textbooks...

5. Nov 28, 2009

### wywong

If you are interested in finding impedance or wave behavior, can you ignore the fact the metals are good conductors?

Wai Wong

6. Nov 28, 2009

### Plutoniummatt

No, the effective permittivity of a metal contains an imaginary term which has dependence on the material's conductivity, for a metal, this is high, therefore the effective permittivity is highly imaginary.

For a non conducting material its low so essentially the imaginary part of the permittivity can be ignored.

And impedance depends on the refractive index....which in turn depends on the permittivity and permeability.