GROUND REFLECTION 



53 



point. There are two types of such rays depending 

 on their state of polarization. If the electric vector 

 is parallel to the reflecting plane, the rays are said 

 to be horizontally polarized and if the electric vector 

 is parallel to a vertical plane through the rays, they 

 are said to be vertically polarized. Wlien consider- 

 ing a very irregular surface, the reflected field may 

 show e.xtreme complexity even though the incident 

 wave is linearly polarized. Increasing roughness 

 may result in diffuse reflection which is ineffective 

 in reinforcing the direct wave. The existence of 

 diffuse reflection depends primarily on the size of the 

 irregularities of the surface in comparison with the 

 wavelength of the incident radiation and on the 

 grazing angle of the incident field. This problem 

 will be discussed in more detail later. 



4.2.3 



Plane Reflecting Surface 



Consider first the simplest case, when a plane 

 wave strikes a plane surface such as that of an 

 absolutely calm sea. The incident ray is then split 

 into two parts. One is the reflected ray, which is 

 returned to the atmosphere, and the other is the 

 refracted ray, which is absorbed by the sea. At the 

 point of reflection, the ratio of any scalar quantity 

 in the reflected wave to the same quantity in the 

 incident wave is defined as the reflection coefficient 

 of the sea for plane waves of given frequency. Thus 

 defined, the reflection coefficient can and will be 

 different for the various components of the field. 



For simpHcity, let us assume the reflecting plane 

 to be the xy plane of a rectangular coordinate system, 

 the xs plane to coincide with the plane of incidence, 

 and the reflection point to be the origin of the 

 coordinate system. 



PLANE OF INCIDENCE 

 ^INCtDENT RAY 



REERACTEO RAY 



Figure 10. Geometry of reflection and refraction. 



For horizontal polarization, the electric vector for 

 the incident wave then is 



where \p is the grazing angle, / the frequency of the 

 radiation and c the velocity of light in free space. 

 The electric vector of the corresponding reflected 

 field is given by the similar expression 



^ _ 2J g-J«-j27r/ I(-(l/c) (icos i// +2sin i|.)] (Ifi^ 



where p and </> are real constants. The ratio of the 

 reflected to the incident field at the reflection point 

 (z = X = 0) is seen to be 



— ^a-3-l' 



R = pe 



(17) 



By definition this is the reflection coefficient for 

 horizontallj'' polarized waves. Thus the reflection 

 coefficient is a complex quantitj^, the amplitude of 

 which is the reflection coefficient of the wave 

 amplitude and the phase is the lag in phase of the 

 reflected wave with respect to the incident wave at 

 the point of reflection. 



The reflection coefficient for vertically polarized 

 radiation is defined in the same way. It is found, 

 however, that the expression of p and (j) in terms of 

 the grazing angle 4/ and the ground constants 

 are quite different for the two types of polarization. 

 For an arbitrary position of the plane of polariza- 

 tion, the wave must be separated into its vertically 

 and horizontally polarized components, and the 

 proper reflection coeflacient applied to each compo- 

 nent separately. 



The quantities p and </> are determined by the 

 boundary conditions for the electric vector at the 

 reflecting surface, namely, that the tangential 

 components of the electric vector on the two sides 

 of the boundary surface shall be eciual. This brings 

 in the ground constants, that is, the conductivity 

 and dielectric constant of the reflecting body. How 

 these boundary conditions are applied may be 

 illustrated by the simple example of horizontally 

 polarized rays reflected from a surface of infinite 

 conductivity. In the surface itself, the sum of the 

 incident and reflected field strength must always 

 be such that the currents set up in the body just 

 suffice to produce the reflected field. Within a 

 reflecting body of infinite conductivity, an infinitely 

 weak field is sufficient, and hence the boundary 

 condition is such that the reflected field, at the 

 reflection point, shall be equal in magnitude and 

 opposite in phase to the incident field, so that the 

 resultant field is zero. Hence for infinite conduc- 

 tivity and horizontal polarization 



Ei = E,e''' 



irf \t-{l/c) {x COS \fj-z sin i//)] 



(15) 



R = - 1, 



p = 1, 4> = 180°. 



(18) 



