How does an index of refraction affect the EM field?

[2sin54]

Hello. Say I have some refraction index n in a homogeneous material. Say I also have equations for the EM field (E and B vectors). Is it true to say that all that changes is the wavelength
$$\lambda \to \frac{\lambda_0}{n}$$
and consequently the wave vector
$$k \to k_0 n ?$$
Is it enough to account for this wavelength change to derive the EM field equations in a homogeneous material of refraction index n?

 

[gleem]

The equation of a one dimensional traveling wave is
∂²A/∂x² = (1/v²)∂²A/∂t²

where v is the velocity of the wave.

Maxwell's wave equation is

∂²E/∂x² = (εμ) ∂²E/∂t²

Where ε and μ are the permittivity and permeability of the material respectively

recognizing that this is a traveling wave equation the velocity of the wave would be

v= 1/(εμ)^½

in a vacuum v =c = 1/(ε₀μ₀)^½

 

[2sin54]

The equation of a one dimensional traveling wave is
∂²A/∂x² = (1/v²)∂²A/∂t²

where v is the velocity of the wave.

Maxwell's wave equation is

∂²E/∂x² = (εμ) ∂²E/∂t²

Where ε and μ are the permittivity and permeability of the material respectively

recognizing that this is a traveling wave equation the velocity of the wave would be

v= 1/(εμ)^½

in a vacuum v =c = 1/(ε₀μ₀)^½

Thank you for the reply. Yes, the velocity changes and consequently both the wavelength and the wave number change as well. So changing the velocity, wavelength and all the functions of these quantities of the EM wave should be sufficient to get the equations of the EM wave in a material, is that correct?

 

[gleem]

So changing the velocity, wavelength and all the functions of these quantities of the EM wave should be sufficient to get the equations of the EM wave in a material, is that correct?

I do not understand your question. The EM wave equation is derived directly for Maxwell's four equations. It relates the spatial variation to the time variation. The solution of the wave equation then provides the velocity. The wavelength and frequency are determined by the source of the wave not the wave equation itself.

 

[2sin54]

I do not understand your question. The EM wave equation is derived directly for Maxwell's four equations. It relates the spatial variation to the time variation. The solution of the wave equation then provides the velocity. The wavelength and frequency are determined by the source of the wave not the wave equation itself.

Sorry for not being clear. I meant to say that I have the equations for the EM wave (in terms of E and B) in a vacuum (n = 1) and I wish to determine the equations for the same wave when it travels through a homogeneous medium (n != 1).

 

[gleem]

The only difference is that ε₀μ₀ is replaced by εμ for the particular medium you are interested in remember

μ = K_mμ₀ K_m = relative permeability

ε= K_eε₀ = K_e = dielectric constant.(relative permittivity )

 

[2sin54]

The only difference is that ε₀μ₀ is replaced by εμ for the particular medium you are interested in remember

μ = K_mμ₀ K_m = relative permeability

ε= K_eε₀ = K_e = dielectric constant.(relative permittivity )

Thank you. That more or less confirms my thoughts.