Fresnel principle

As one can see from relation (13.112), the wavefield at the point r D may be viewed at the moment of time t as the sum of elementary fields of point and dipole sources distributed over the surface S with densities dP r,t)/dn and P r,t) respectively. The interference of these fields beyond the domain D results in complete suppression of the total wavefield. Thus, the Kirchhoff integral formula can be treated as the mathematical formulation of the classical physical Huygens-Fresnel principle. 

A second method utilizes the Fresnel principle (Figure 19-44), which relates the transmittance of a dielectric interface to the refractive indices of the interface materials. Such an interface may be formed between a glass prism of selected optical properties and the liquid whose refractive index is to be measured. These detectors are difficult to use with gradient elution systems, and temperature control of the solvents is critical. 

Huygens-Fresnel principle Every point on a primary wavefront serves as the source of secondary wavelets such that the wavefront at some later time is the envelope of these wavelets. 

Figure 3. Detector cell utilizing the Fresnel principle.

We need to point out that, if the wavelengths of laser radiation are less than the size of typical structures on the optical element, the Fresnel model gives a satisfactory approximation for the diffraction of the wave on a flat optical element If we have to work with super-high resolution e-beam generators when the size of a typical structure on the element is less than the wavelengths, in principle, we need to use the Maxwell equations. Now, the calculation of direct problems of diffraction, using the Maxwell equations, are used only in cases when the element has special symmetry (for example circular symmetry). As a rule, the purpose of this calculation in this case is to define the boundary of the Fresnel model approximation. In common cases, the calculation of the diffraction using the Maxwell equation is an extremely complicated problem, even if we use a super computer. 

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. 

Two other types of RI monitor are based on Fresnel s laws of reflection and the principle of interferometry respectively. The former utilizes a very small volume (3 pi) sample cell and is therefore useful for highly efficient columns, but linearity is limited and the cell windows need to be kept scrupulously clean for optimum performance. The main advantages of the interferometric design are improved sensitivity and a wide linear range. 

The opacity of plastic foams, and polymers with scratched surfaces, is also governed by Fresnel s law. The n value of the gas which occupies the scratch indentation is much lower than that of the polymer. Light may be directed through rods of transparent polymers, such as PMMA. This effect may be enhanced when the rod or filament is coated with a polymer with a different refractive index, such as polytetrafluoroethylene (ptfe). Optical fibers utilize this principle. 

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... 

Some attention has to be given to the degree of circular polarization y and thus to the creation of cpl. Two experimental principles are common the use of a quarter wavelength plate and the use of a Fresnel rhomb or a Solcil-Babinet compensator in a few experiments, radiation from a cyclotron after passage through a polarizing undulator was used. The degree of circular polarization is easily jeopardized when a X/4 plate is employed, as this is an interference device... 

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... 

Consider surfaces that are inert and may be made (molecularly) smooth, so that, optically speaking, they may be treated as Fresnel surfaces. Mica, certain polished glasses, quartz and silicon wafer surfaces may belong to this category. For such well-defined systems the optical techniques introduced in sec. 1.7.10 come to mind reflectometry, ellipsometry, and (to study the dynamics) fluorescence recovery after photobleaching (FRAP). The principles of these techniques have been outlined in that section. 

We can use Huygens principle to explain qualitatively the essential features of diffraction, but a quantitative treatment involves casting Huygens principle into a precise mathematical form, the Fresnel-Kirchhoff formula ... 

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