Solution

a) Perpendicular component of the electric field

When the wave is incident on the boundary, the electric field displaces charges inside the dielectric, causing induced surface charges to accumulate at the interface. These charges generate an additional electric field that, inside the medium, is perpendicular to the surface and opposes the incident field. Consequently, only the perpendicular component of the electric field intensity $\mathbf{E}$ is reduced by a factor$\varepsilon$. The parallel component, not being affected by these charges, does not change.

b) Parallel component of the magnetic induction

The time variation of the wave's electric field produces induced surface currents at the boundary. These currents create an additional magnetic field that, inside the medium, is parallel to the surface and reinforces the magnetic field of the incident wave. Therefore, only the parallel component of the magnetic induction $\mathbf{B}$ increases by a factor $\mu$. The perpendicular component is not altered by these currents and remains unchanged.