Electromagnetic waves > Properties of emission and reflection of electromagnetic waves > Problem 12.1.31

Statement

$12.1.31.$

Why is it that when an electromagnetic wave passes through a flat vacuum
— nonconducting medium boundary: a) the component of the electric field
strength perpendicular to the boundary decreases by a factor ε, but the par-
allel one does not change; b) the component of the magnetic field induction
perpendicular to the boundary does not change, but the parallel one increases
by a factor µ? ε is the dielectric constant and µ is the magnetic permeability
of the medium.

Solution

When an electromagnetic wave is incident on the plane boundary between vacuum and a non-conducting medium, charges and currents are induced at the interface surface. These secondary sources generate additional fields which, when superposed on the incident field, modify the components of the total field within the medium.

a) Electric field

The incident wave sets the electrons of the medium in motion, causing an accumulation of induced surface charges at the interface. These charges create an additional electric field that, inside the medium, is perpendicular to the boundary and opposes the incident field. As a result, only the perpendicular component of the electric field is reduced by a factor $\varepsilon $(the relative permittivity of the medium). The parallel component is not affected by these charges and remains unchanged.

b) Magnetic field

The time variation of the wave's electric field generates induced surface currents at the boundary. These currents produce an additional magnetic field that, inside the medium, is parallel to the surface and reinforces the incident magnetic field. Consequently, only the parallel component of the magnetic induction$ \mathbf{B}$ increases by a factor $\mu $(the relative permeability of the medium). The perpendicular component, not being affected by these currents, remains the same as in vacuum.