Normal incidence

For normal incidence, we have that 0, = 0 = 0 = 0. In this case the parallel or perpendicular orientations coincide and the plane-wave transmitted in the second medium is uniform. Considering the power (i.e. from the Po3mting vector) instead of the amplitude coefficients, we obtain the reflectance (R) and the transmittance (T) 

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Each reflector contributes a reflection along a raypath to the surface, defined by the normal incidence reflection point (shortest travel time)... 

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

In this section, two illustrative numerical results, obtained by means of the described reconstruction algorithm, are presented. Input data are calculated in the frequency range of 26 to 38 GHz using matrix formulas [8], describing the reflection of a normally incident plane wave from the multilayered half-space. 

Another important consideration for providing uniform implantation involves the geometry of the ion beam with respect to the target surface. Too high an angle from normal incidence leads to excessive sputtering and low retained dose. These issues and others pertinent to practical aspects of implantation treatment have been discussed (35,165). 

Special contact transducers having wedges providing incidence angles for specific appHcations are used widely in industry. For example, normal incidence is used in tests for laminations within sheets, and for sheet or plate thickness where the back surface of the test material parallels, to within perhaps 10°, the front surface. Shear wave transducers typically used for weld examination have 45°, 60°, or 70° inspection (refracted) angles. To locate discontinuities, the transducers may be moved back and forth over selected surface areas until the angled search beam approaches normal incidence on the... 

Many problems of practical interest are, indeed, two dimensional in nature. Impact and penetration problems are examples of these, where bodies of revolution impact and penetrate slabs, plates, or shells at normal incidence. Such problems are clearly axisymmetric and, therefore, accurately modeled with a two-dimensional simulation employing cylindrical coordinates. 

Eulerian codes are often used to simulate high-velocity impact and penetration events, such as shown in Fig. 9.26. Here the problem involves the penetration of armor steel by a tungsten projectile at normal incidence. 

Rgure 5 NEXAFS spectra above the C K-edge for a saturation coverage of pyridine C5H5N on Pt(111), measured at two different polarisation angles with the X-ray beam at normal incidence and at 20° to the sample surface. 

Figure 5 Si backscattering yiaids (anguiar scans) for normal incidance on the Si (111) (7x7) surface (solid squares) and the Si (111) [Jz x Jz) R30°-Au surface (open circies). The curve is the expected yield from a bulk terminated Si (111) surface. The scattering geometry is shown in the inset.

Figure 10 SIMS depth profiles with end without sample rotation during bombardment by 3-keV O2 at 40° from normal incidence. ...

There is no MOKE response for normally incident p- or j-light in either the longitudinal or transverse geometries. 

There is a latter MOKE response at normal incidence for the polar geometry than for oblique angles. 

For transparent plastics materials transparency may be defined as the state permitting perception of objects through or beyond the specimen. It is often assessed as that fraction of the normally incident light transmitted with deviation from the primary beam direction of less than 0.1 degree. 

Figure 15.8. Light transmission of acrylic polymer (5 in thick moulded Diakon. Parallel light beam normally incident on surface). (Reproduced by permission of ICI)...

Data collection is mostly performed at normal incidence of the primary electron beam. Under these conditions usually several equivalent LEED spots exist because of the surface symmetry. By taking care that the I-V curves of equivalent spots are identical, normal incidence conditions can be adjusted to within a few tenths of a degree. 

Observation of absorption bands due to LO phonons in RAIR spectra of thin, silica-like films deposited onto reflecting substrates demonstrates an important difference between RAIR and transmission spectra. Berreman has shown that absorption bands related to transverse optical (TO) phonons are observed in transmission infrared spectra of thin films obtained at normal incidence [17]. However, bands related to LO phonons are observed in transmission spectra of the same films obtained at non-normal incidence and in RAIR spectra. Thus, it is possible for RAIR and transmission spectra of thin films of some materials to appear very different for reasons that are purely optical in nature. For example, when the transmission infrared spectrum of a thin, silica-like film on a KBr disc was obtained at normal incidence, bands due to TO phonons were observed near 1060,790,and450cm [18]. 

Fig. 11. Simulated diffraction space of a chiral (40, 5) SWCNT. (a) Normal incidence diffraction pattern with 2mm symmetry (b),(c),(d) and (e) four sections of diffraction space at the levels indicated by arrows. Note the absence of azimuthal dependence of the intensity. The radii of the dark circles are given by the zeros of the sums of Bessel functions [17].

Several sections of the diffraction space of a chiral SWCNT (40, 5) are reproduced in Fig. 11. In Fig. 11(a) the normal incidence pattern is shown note the 2mm symmetry. The sections = constant exhibit bright circles having radii corresponding to the maxima of the Bessel functions in Eq.(7). The absence of azimuthal dependence of the intensity is consistent with the point group symmetry of diffraction space, which reflects the symmetry of direct space i.e. the infinite chiral tube as well as the corresponding diffraction space exhibit a rotation axis of infinite multiplicity parallel to the tube axis. 

Fig. 12. S imulated diffraction space for a (10, 10) armchair tube, (a) Normal incidence pattern, note the absence of oo.l spots, (b) Equatorial section. The pattern has 20-fold symmetry, (c) The section The pattern contains 20 radial...

Fig. 13. Simulated diffraction space of a 10-layer monochiral MWCNT with Hamada indices (40+8/ , 5+k) with / =0,...,9. In (a), (a ) and (02) the initial stacking at ( q was ABAB. whereas in (b), (b[) and (b2) the initial stacking was random, (a) The normal incidence pattern has a centre of symmetry only. (3 )(a2) The cusps are of two different types. The arc length separating the cusps is c (b) The normal incidence pattern now exhibits 2mm symmetry. (b )(b2) The cusps are distributed at random along the generating circles of the evolutes. These sections represent the diffuse coronae referred to in the "disordered stacking model" [17].

Figure 5. Effect of the incidence angle on the spectral profile of a transmission coating. G normal incidence. R p-polarization. B s-polarization.

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