Refractive Index: Variations & Formula Proof

[alikazemi7]

Hi
1)Does refractive index varies when we are dealing with different waves? for example the refractive index for a typical glass is 1.5 when a visible light passes through it. Does it the same for x rays?
2) there is a complex formula which describes the refractive index: n = 1- δ - iβ. how is the proof of this formula?

 

[ViolentCorpse]

1) Yes refractive index of a material varies with wavelength of the radiation incident on it.

Can't answer the 2nd question.

 

[Tahmeed]

Refractive index changes with variation of waves, yes. And that formula looks familiar, I think I saw it in Feynman's lecture in physics, but I don't think the proof was given there, the proof may be too complex.

 

[vanhees71]

A quite simple model for the dielectric function of a homogeneous material (and thus the refraction index) is to assume a completely classical system of bound charges, which are only slightly disturbed by the incoming electromagnetic wave and thus linear-response theory is applicable. So you can just assume that the charges of the material are bound harmonically and have some "friction" (dissipation). It's a bit lengthy to work this out here. You find an excellent treatment of this classical dispersion theory in

A. Sommerfeld, Lectures on theoretical physics, vol. 4 (optics)

 

[blue_leaf77]

2) there is a complex formula which describes the refractive index: n = 1- δ - iβ. how is the proof of this formula?

In general, refractive index can be complex, i.e. $n=n_R+i\hspace{0.5mm}n_I$. This is because refractive index is defined as the square root of permittivity, while permittivity is a complex quantity.
$$
n=\sqrt{\epsilon} = \sqrt{1+\chi} = \sqrt{1+\chi_R+i\hspace{0.5mm}\chi_I}
$$
So, it's no surprise that you would find something like you wrote there.