Fresnel relationships

For most materials the reflected energy is only 5-10%, but in regions of strong absorptions the reflected intensity is greater. The data obtained appear different from normal tra(nsmission spectra, as derivative-iike bands result from the superposition of the normal extinction coefficient spectrum with the refractive index dispersion (based upon the Fresnel relationships from physics). However, the reflectance spectrum can be corrected by using the Kramers-Kronig (K-K) transformation. The corrected spectrum appears similar to the familiar transmission spectrum. 

At mirror surfaces, incident radiation can be reflected regularly. This reflectivity (the ratio of the reflected to the incident radiation power) depends on the refractive indices of the two layers forming the interface [96,98]. According to the Fresnel relationships, the reflectivity is given by... 

Although measurements of refractive index can be inferred by applying the Fresnel relationship to the measured reflectance values, this is an imprecise method. Instead, methods such as immersion in liquids and measurement of the Brewster angles are generally used. 

Flere the Fresnel transfonnation describes the relationship between the electric field /iciin medium 1... 

No pure compound with a peak at 375 m/j has been found to date, but occurrence of this peak certainly suggests that the compound responsible is related to the furfurals. An optical relationship also exists. When the colorant index is plotted against the frequency, the two peaks of 5-(hy-droxymethyl)-2-furaldehyde are found at 1305 and 1055 fresnels (sec.-1 X 1012). The peak of the unknown is at 805 fresnels, which is an exact, harmonic difference. The next harmonic would be at 555 fresnels or 540 m/j, in the general region in which the minima are found. The harmonic possible at 540 m/i is, unfortunately, in the region where light-scattering phenomena must also receive consideration. 

Of interest is the light intensity measured on plane II, located a distance / from plane I. Huygen s principle simply states that the field at plane II is the sum of spherical waves emanating from all points in plane I. However, the field at point A will be primarily influenced by the spherical wave at point A, with a similar relationship between the fields at points B and B. Fresnel s extension of Huygen s principle quantifies this statement. The spherical wave emanating from a differential area, dS, located at point A is... 

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). 

For n layers, the matrices for each layer are multiplied together, [C] = [Ci][C2]. .. [C + i], to give the resultant reflectivity from the elements of the final 2x2 matrix such that, R = cc jaa. In practice, recurrence relationships between the Fresnel coefficients in the successive layers can be used to provide an efficient calculation. Furthermore, following the approach of Nevot and Croce [20], a Gaussian roughness or diffuse profile can be included at each interface in the stack, such that... 

Frequently used combinations of groups, 141 Fresnel s relationship, 297 Friction, 840 coefficient, 831 Fringed micelle model, 29 Fugacity, 756 coefficient, 756... 

The physical principle of these polarizers rests on the so called Brewster reflection that is theoretically explained by the Fresnel theory of reflection and refraction. Each dielectric medium reflects at a definite angle called Brewster angle, only radiation which is polarized perpendicularly to the plane of incidence. The Brewster angle is determined by the refractive index of the medium according to the relationship tan The... 

The relationship between the reflectance from an interface between two transparent media and their respective refractive indices is given by Fresnel s equation. 

Optical theory includes the Fresnel equations that describe the behavior of light waves at an interface between media of differing refractive index, and other relationships between the atomic scattering factors and absorption cross sections. It can be applied to X-ray reflectivity and refraction in the critical angle region. 

According to Fresnel, the relationship between the intensity of the reflected light /, and the intensity of the incident light /q involves the angle of incidence a and the angle of refraction p (for angle definitions, see Figure 15-1) ... 

In order to determine the refractive index (R2) and the thickness (t) of a surface film, one measures A and of the light reflecting from the film-covered surface. For a transparent film the relationship between the film properties (02, t) and the ellipso-metric measurements (A, ij/) is given by Eqs. (5a)-(7) and the Fresnel equations (2a) and (2b). From these equations, /I2 and t can be determined from A and (Note that Eq. (7) is two equations since there are real and imaginary parts.) However, an analytical solution for 2 and t is not possible because the equations... 

The relationships between E, H, and the incident beam fields Ej and H are provided by the Fresnel reflection coefficients for plane-wave reflection at a dielectric interface, discussed in Section 35-6. In general, these coefficients depend on the polarization of the beam, but, if 0j is small, they are independent of polarization and are given by Eq. (35-18) with d replaced by Ujand... 

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