Fresnel interfaces

Frenkel defects 3.173 Fresnel equations 1.7.10a Fresnel Interfaces 1.7.73, 2.5c... 

For a Fresnel interface, the density profile is a step function and the Fourier transform equals (Ap) /q, with Ap the difference in density between the two phases. Thus, in the Bom approximation. 

The Fresnel refractometer which measures the change in the fractions of reflected and transmitted light at a glass-liquid interface as the refractive... 

Deviation refractometers are the most commonly used. This version of the DRI measures the deflection in the location of a light beam on the surface of a photodiode by the difference in refractive index between the polymer solution and pure solvent. The Fresnel-type refractometers operate on the principle that the intensity of light reflected from a glass-liquid interface is dependent on the incident angle and the RI difference between the two phases. The deviation and Fresnel detectors typically have cell volumes of 5 to 10 pi, detection limits of about 5 x 10-6 refractive index units (RIU), and a range of 10 7 to 10 3 RIU.156 The deflection-type DRI is relatively insensitive to the buildup of contaminants on the sample cell and is therefore of special utility in laboratories that process large numbers of samples, such as industrial laboratories. 

Specular reflection of electromagnetic radiation at the (electrochemical) interface is generally described by Fresnel equations. Supposing the most simple case that both the electrolyte and electrode are transparent and differ only in their refractive indexes, nx and n2, the reflectivity for normal incidence of the radiation equals ... 

The approximate picture of a transparent electrochemical interface is rather far from the actual situation. Nevertheless, the Fresnel equations are valid also for absorbing media, if one uses the complex refractive indexes, Nk ... 

The authors assumed a model of the various interfaces as shown in Figure 2.82(b). The Si was the underlying substrate on which the copper electrode was deposited. Such a structure will give rise to the reflections as shown, each one characterised by a wavevector transfer for both sides of the interface at which the reflection occurs. By applying the Fresnel equations to the reflections in the model in Figure 2.82(b), the reflectivity R can be derived. 

In this section we derive an approximate expression for the absorption cross section of a large weakly absorbing sphere. We assume that the incident plane wave can be subdivided into a large number of rays the behavior of which at interfaces is governed by the Fresnel equations and Snell s law (Section 2.7). A representative ray incident on the sphere at an angle 0, is shown in Fig. 7.1. At point 1 on the surface of the sphere the incident ray is divided into externally reflected and internally transmitted rays these lie in the plane of incidence, which is determined by the normal to the sphere and the direction of the incident ray. If the polar coordinates of point 1 are (a, 0f, ), the plane of incidence is the plane = constant. At point 2 the transmitted ray encounters another boundary and therefore is partially reflected and partially transmitted. In a like manner we can follow the path of the rays within the sphere, a path that does not deviate outside the plane of incidence. At each point where a ray encounters a boundary it is partially reflected internally and partially transmitted into the surrounding medium. On physical grounds we know that the absorption cross section cannot depend on the polarization of the incident... 

Fresnel Reflection—The reflection of a portion of the light incident between two homogeneous media having different refractive indices. Fresnel reflection occurs at the air/glass interfaces at entrance and exit ends of an optical fiber. 

At each air-film, film-film, or film-substrate interface, the incident light amplitude is split into a reflected and a transmitted fraction according to die Fresnel coefficients... 

Ie is the true scattered intensity I e is the measured scattered intensity at angle 6, and Z i8o-e is at the supplementary angle. fa and fi are the Fresnel s coefficients for the fractions of light reflected at perpendicular incidence at the glass-air and glass-liquid interfaces, respectively ta and tx are the corresponding transmission coefficients. They are defined by the following equations ... 

An example of the use of Fresnel defocus imaging, diffuse dark field imaging and HRTEM to examine the same SiC-SiC interface is shown in Fig. 17.1 (Turan, 1995). All three techniques clearly indicate the presence of... 

However, when HRTEM was employed on the SiC samples, which showed a similar contrast variation across SiC grain boundaries in the SEM, the presence of residual intergranular films was not detected even at the triple junctions. Hence, Kleebe concluded that SEM imaging and Fresnel fringe TEM imaging alone do not enable a safe conclusion to be drawn about interface wetting in ceramic polycrystals. 

Equations (1.74) to (1.77) are the Fresnel formulae. Examination of equation (1.77) reveals that light with p polarization will not be reflected from a plane interface (/ = 0) at a specific angle of incidence, Brewster angle and, for the case... 

Here, n and n2 are the refractive indices of the interfacing materials. The surface reflectivity R, Equation 5, used by Robinson is the Fresnel reflectivity for normal light incidence (c.f. 4). Robinson s interpretation explains the well-known linear relationship between the specific surface area of a paper, as measured by gas adsorption, and its scattering coefficient (15. 28, 32). It also rationalizes the observed decrease in scattering and brightness of wet compared to dry pulp (33, 34). 

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