Relationship between Refractive index and Inpedance

[Plutoniummatt]

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

 

[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

 

[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

 

[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 what's in the textbooks...

 

[wywong]

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

Wai Wong

 

[Plutoniummatt]

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

Wai Wong

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.