Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 54

Assume the ionosphere to be modeled by a plasma region with an electron density that increases with altitude from a low value at the lower boundary toward a value N max and decreases again as the altitude gets higher. A plane electromagnetic wave impinges on the lower boundary at an angle i with the normal. Determine the highest frequency of the wave that will be turned back toward the earth. (Hint: Imagine the ionosphere to be strat­ified into layers of successively decreasing constant permittivities until the layer containing N max. The frequency to be determined corresponds to that for an emerging angle of /2.)