When EM radiation is travelling between the media of different refractive indices, parts of it are reflected and transmitted according to Fresnel's equations. The amount of reflectivity and transmittance depends on the polarization of incoming radiation. In the derivation of those equations we assume the continuity of components tangential to interface of electric and magnetic fields. Is there continuity only in the tangential or also in components perpendicular to interface? And also I would like to have a physical explanation in terms of rays or waves by which I can imagine the phenomena.

When EM radiation is travelling between the media of different refractive indices, parts of it are reflected and transmitted according to Fresnel's equations. The amount of reflectivity and transmittance depends on the polarization of incoming radiation. In the derivation of those equations we assume the continuity of components tangential to interface of electric and magnetic fields. Is there continuity only in the tangential or also in components perpendicular to interface? And also I would like to have a physical explanation in terms of rays or waves by which I can imagine the phenomena.