A block of glass, refractive index n=κ, fills the space y>0, its surface being the xz plane. A plane wave traveling in the positive y direction through the empty space y<0 is incident upon this surface. The electric field in this wave is z^Eisin(ky−ωt). There is a transmitted wave inside the glass block, with an electric field given by z^Etsin(k′y−ωt). There is also a reflected wave in the space y<0, traveling away from the glass in the negative y direction. Its electric field is z^Ersin(ky+ωt). Of course, each wave has its magnetic field, of amplitude, respectively, Bi, Bt, and Br.
The total magnetic field must be continuous at y=0; and the total electric field, being parallel to the surface, must be continuous also (see Problem 10.14). Show that these requirements, and the relation of Bt to Et given in Eq. (10.83) (with the ``0'' subscript changed to ``t''), suffice to determine the ratio of Er to Ei. When a light wave is incident normally at an air--glass interface, what fraction of the energy is reflected if the index n is 1.6?