Why is the index of refraction dependent on the dielectric constant

[Kidphysics]

and frequency? Could someone point me in a direction where this is explained in depth? I understand polarization and the dielectric constant as I've taken E&M 1

 

[nkyall]

Dielectric changing index of refraction

I would say that it is dependent on the dielectric constant because as an EM wave travels through any medium the dielectric constant will change the way the wave propagates through that medium. See the wikipedia page: http://en.wikipedia.org/wiki/Refractive_index#Dielectric_constant where n = √ε_{0}μ_{0}. As ε_{0}changes with different materials so will the refractive index.

 

[Kidphysics]

thank you I guess I just have to think about it. It seems like the dielectric constant is a measure of polarize ability and this could retard an EM wave?

 

[nkyall]

No worries. However, I need to correct myself with what I said. n = √ε_{r}μ_{r} where ε_{r} "is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum" (taken from: http://en.wikipedia.org/wiki/Relative_permittivity) and μ_{r} is "Relative permeability...is the ratio of the permeability of a specific medium to the permeability of free space,μ_{0} " (taken from: http://en.wikipedia.org/wiki/Permea...tive_permeability_and_magnetic_susceptibility). This says that the index of refraction will ultimately depend on the EM wave's behavior as tested in an applied voltage and magnetic field. I wouldn't necessarily say it has anything to do with polarizability though as that is dealing with which plane the electric field or magnetic field is oscillating in (e.g. unpolarized waves oscillate in the xy plane if the wave propagates in the z direction). I hope this helps a little and sorry for the initial incorrect definition of n.

 

[Kidphysics]

ah but I meant the polarizability of the substance like a dielectric! Not the plane of oscillation

 

[nkyall]

Ahhhhhh! Yes you are correct. My apologies on the misinterpretation.

 

[Kidphysics]

Ahhhhhh! Yes you are correct. My apologies on the misinterpretation.

no problem. Do you think that is how εr changes the index of refraction?

 

[nkyall]

Yes I do. I have been wrong before though but I am going off of what I looked up and how I interpret it.