6

REFLECTION AND REFRACTION

6.1 INTRODUCTION

In many situations, Earth terrain and/or the atmosphere may be modeled as consisting of layers of dielectric media separated by planar or spherical interfaces. Analytical models for such configurations are well established [1–3]: the basic formalisms of reflection and refraction for a planar boundary are reviewed in this chapter to prepare for their application to path loss predictions in subsequent chapters. The basic theory of refraction derived in this chapter is also applied to study the propagation of electromagnetic waves in an inhomogeneous atmosphere above a spherical Earth, and the ducting phenomena that can result are investigated.

6.2 REFLECTION FROM A PLANAR INTERFACE: NORMAL INCIDENCE

Consider an interface between two linear, homogeneous, isotropic, and time-invariant media located in the xy plane as shown in Figure 6.1. Regions 1 and 2 are located above and below the interface, respectively, and are characterized by i, μi, and σi where i = 1, 2. Our experience tells us that a wave that encounters a boundary with a different medium will have some portion of its energy reflected from the boundary while the remainder is transmitted; for example, in a piece of glass one can see both reflected light (forming an image of the observer) and light transmitted from the other side. A determination of how much energy is reflected given the properties of the two media, however, requires use of electromagnetic theory and is considered ...

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