When we derived the proportion of energy in an electromagnetic plane wave reflected during normal incidence we found two of the boundary conditions played no role. Explain why this is.

When we derive the proportion of energy in an electromagnetic plane wave reflected during normal incidence, we use the boundary conditions of Maxwell's equations. These boundary conditions are derived from the continuity of the tangential components of the electric and magnetic fields across the boundary.

However, during normal incidence, the direction of propagation of the wave is perpendicular to the boundary. This means that there are no tangential components of the electric and magnetic fields, as they are both parallel to the direction of propagation and thus perpendicular to the boundary.

Therefore, the boundary conditions that involve the tangential components of the electric and magnetic fields play no role in the derivation of the proportion of energy reflected during normal incidence. This is because these components are zero due to the geometry of the situation.

In other words, the boundary conditions that are relevant are those that involve the normal components of the electric and magnetic fields, as these are the components that are non-zero during normal incidence.