Degeneracy of Fresnel Reflection Coefficients at Normal Incidence.

Luc Lévesque

Royal Military College of Canada

The Fresnel reflection coefficients are revisited by choosing consistent directions for the relative electric field orientations normal and parallel to the plane of incidence. The boundary conditions are applied at the interface between two semi-infinite uniform media. This leads us to the conclusion that the reflection coefficients for both the s and p waves are equal at normal incidence, in agreement with the treatment presented in some textbooks. A different convention is also used in other textbooks and gives Fresnel reflection coefficients that are of opposite signs. These contradictory results have no implications on the reflectivity at an interface, which equals the square of each Fresnel coefficient, but is changing the phase of the electric field reflected at the interface. It is believed that the considerations being examined, which are based upon symmetry, will be useful to university or college teachers when introducing Fresnel’s equations in the classroom.