Angles of incidence and observation

Cholesteric liquid crystals, e.g., those of cholesteroylnonaoate (see Sec. 3.2), produce a Bragg-type scattering, which depends on temperature and angles of incidence and observation. Either total reflection or total transmission of circular polarized light is observed, which effect provides the basis of the dark-bright liquid crystal display in the Schadt-Helfrich cell (Fig. 3.5.3) as well as color reflection. 

In reflection of radiation at solid matte surfaces, diffuse and specularly reflected energies are superimposed. The intensity of the diffusely reflected energy is dependent on the angles of incidence and observation, but also on the sample packing density, sample crystalline structure, refractive index, particle size distribution, and absorptive qualities. Thus, an ideal diffusely reflecting surface can only be approximated in practice, even with the finest possible grinding of the samples. There are always... 

Hector Mcl. Clark and associates (Clark et al., 2000 Clark and Wong, 1995) developed a wear tester based on a high-speed disk and on a slurry pot to evaluate the nature of erosive wear. Another type of slurry pot test was described by the U.S. Bureau of Mines (Blickensderfer et al., 1987) where only a very low angle of incidence was observed. 

This is the familiar formulation of Bragg s law for a three-dimensional point lattice. It says that the Fourier transform of a point lattice is absolutely discrete and periodic in diffraction space, and that we can predict when a nonzero diffraction intensity will appear for any family of planes hkl, and what the angle of incidence and reflection 0 must be in order for an intensity to appear. Bragg s law, notice, is completely independent of atoms, or molecules, or unit cell contents. The law is imposed by the periodicity of the crystal lattice, and it strictly governs where we may observe any nonzero intensity in diffraction space. It tells us when the resultant waves produced by the scattering of all of the atoms in the many individual unit cells, each represented by a single lattice point, are exactly in phase. 

The main point to be made here is that the phase shift data obtained from spectral interferometry has two contributions surface motion and optical effects. These two contributions to the phase versus time data can be separated by performing these experiments at two angles of incidence and two polarizations, at technique we term ultrafast d3mamic ellipsometry. The optical effects during shock breakout in nickel films were hidden because they produce phase shifts of the same sign as that caused by surface motion. Ultrafast dynamic ellipsometry allowed that contribution to be measured [71]. In our experiments on bare metals, the observed optical effects are due to changes in the material s complex conductivity under shock loading. We will see below that this is only one of several kinds of optical effects that can be observed in these and other materials. 

Brewster s law. Reflected light in general is more polarised than the incident light and according to Brewster s law, the polarisation is maximum when i + r = 90 where i and r are the angles of incidence and refraction. There are several methods described in the literature such as those based on the use of prisms and fluid immersion (in fluids of known refractive indices) and index matching. The so-called Becke line technique for index matching uses observations under microscope. 

About 1600 A.D. combinations of lenses were used and the telescope was invented about 1609 in Holland. News of this development reached Galileo in Italy and he improved on the telescope and demonstrated his own in 1610. This is also about the time that Snell (1591-1626) made his observation of the sine relationship between the angles of incidence and reflection as light passed between two different media. 

Thus, the reflected radiance is the integral of the energy in each incident direction times the BRDF for that particular combination of incidence and observation angles under consideration. The BRDF, or in short the reflectance, plays a central role in the remote sensing of planetary surfaces and is important for the correct assessment of their albedo. 

Figure 6.16 Refraction of a chemical wave, (a) Experimental observation in a silica gel layer open to air, with stepwise variation in thickness, (b) Schematic representation of part a ab, boundary between regions / (thickness = 2.15 mm) and R (thickness = 1 mm) i, - and v, wave vectors of incident and refracted waves, respectively

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