Reflection, law

One can distinguish the surface and volume components in the diffuse transmission /dt and the diffuse reflection /dr (Fig. 1.22) [224-227]. The surface component, which is referred to as Fresnel diffiise reflectance, is the radiation undergoing mirrorlike reflection and still obeying the Fresnel reflection law but arising from randomly oriented faces. This phenomenon was first described by Lambert in 1760 [228] to account for the colors of opaque materials. The volume, or Kubelka-Munk (KM), component is the radiation transmitted through at least one particle or a bump on the surface (Fig. 1.22). 

Fig. 53. Because of the Bragg reflection law large network plane distances correspond to small angles of diffraction and vice versa.

The curve in Fig. 56b shows entirely different conditions. The first maximum is displaced much nearer to the point of penetration. This indicates the very frequent occurrence of some distance in the liquid which exceeds the intramolecular distances of the individual atoms for according to Bragg s reflection law... 

The principle is extremely simple, in that a collimated laser beam is directed under an angle Om into a pair of parallel, plane mirrors. According to the optical reflection law from plane surfaces, the beam bounces back and forth between the two mirrors Ma and Mg, always maintaining the same angle. It finally emerges under the same angle, but mirrored in direction from the input beam (ain = —aout), as shown in Figure 6.10. The number of passes can be altered in two ways. 

Fig. 6. The angular reflected energy distribution for the Lambert cosine law versus the Seeliger diffuse reflectance law.

Seeliger (in 1888) derived a diffuse reflectance law based on the assumption that the radiation striking the surface of a powder will penetrate into the interior of the powder sample and thus does not represent a perfect remitting (Lambertian) surface (Fig. 6). 

The Knudsen number Kn, defined as the ratio between the mean free path of the molecules and the characteristic length of the system, is often used to establish the domain level of the phenomenon and limits in the model application ranges. For Kn 1 the usual continuum modeling is valid. Satisfactory prediction of experimental results can be obtained until Kn = 0.3, but the question is raised as to whether it is possible to further extend the continuum modeling accounting more correctly for surface phenomena like the reflection law, and the Knudsen layer, or whether the validity limit of the continuum approach is reached here [3]. 

In general, each vector equation stands for six equations, one for each component of E and H in the three coordinates, but the number can be reduced by proper choice of the coordinate system. In setting all (j)j equal in the above equations we tacitly imply the validity of the reflection law. As in the discussion of the Fresnel equations we solve the problem for two orthogonal, linearly polarized waves. Other states of polarization may be represented by superposition of these solutions. For the transverse E wave (TE) the electric vector is perpendicular to the plane of incidence, and only the z-component of E exists, = E . The same is true for the transverse H wave (TM), where only the = H component is present. 

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