Asimple model of propagation of radio waves in the earth’s atmosphere or ionosphere consists of a flat earth at z = 0 and a nonuniform medium with = (z) for z > 0. consider the maxwell equations under the assumption that the fields are independent of y and can be written as functions of z times e i(kx−ωt) . (a) show that the wave equation governing the propagation for z > 0 is d 2f dz2 + q 2 (z)f(z) = 0 where q 2 (z) = ω 2 c 2 (z) − k 2 and f = ey for horizontal polarization, and where q 2 (z) = ω 2 c 2 (z) + 1 2(z) d 2 dz2 − 3 4 2(z) d dz 2 − k 2 and f = √ ez for vertical polarization