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So, we were ask to consider the Fresnel Equations for parallel and perpendicular waves (with index of refractions).

Then, we are ask to prove some equations in which "... for nonmagnetic non-conductors"

The Fresnel equations got reduced and the indexes of refraction disappeared. I do not really know where to start, but in our reference book we have: normal incidence and oblique incidence topics.

Any help?

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It's a simplification. Typically, you use boundary conditions to relate the fields outside and inside the dielectric that say that the normal component of the electric field $\mathbf{E}$ has a discontinuity so that the auxiliary field $\mathbf{D}$ is continuous. There is also another condition that says that the tangential component of $\mathbf{E}$ is continuous across the boundary. Since $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$, I don't think this continues to be the case if $\mathbf{B}$ has a discontinuity, as will be the case in a magnetic material. In a magnetic material, the $\mathbf{B}$-field jumps at the boundary owing to an induced surface current density. Look at Jackson or Griffiths for details on these boundary conditions.

Similarly, the material being non-conducting means that you don't have to worry about things like a current-density $\mathbf{J} = \sigma \mathbf{E}$ being induced by the electric field. However, I have a suspicion that the non-conducting requirement is not really necessary, since you can incorporate the conductivity $\sigma$ into the electrical permittivity (look up, for example, the Drude model in Jackson).

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