Scattering specular reflection

Beer s law applies where refractive index, scattering specular reflection at infinite-finite numbers of surfaces all obey the Fresnel formulas. A definite reflectance theory does not exist, as the convolution of an infinite number of integrals would be required to describe all the combined light interaction effects at all surfaces under varying conditions. Thus, Beer s law is often shown to illustrate the properties of NIR spectroscopy for lack of an ideal model. 

Figure A3.9.4. The ratio of specular reflectivity to incident beam intensity ratio for D2 molecules scattering from a Cii(lOO) surface at 30 K [21],...

If, instead of assuming diffuse reflection at the wall, it is postulated that a fraction f of the incident molecules is scattered diffusely and the rest suffer specular reflection, the right hand side of equation (2.8) must be multiplied by a factor (2 - f)/f. ... 

Figure 13 The contrast between (a) specular reflection and (b) cosine law scattering.

The average incident tangential momentum is muh while the average scattered tangential momentum is muf. If the gas molecule equilibrates with the surface and the scattered momentum is zero, we have Knudsen cosine scattering and complete accommodation of the incident gas molecule with the surface. On the other extreme, if specular reflection occurs, the incident momentum is retained upon scattering and mut = muf. The momentum accommodation coefficient, / is introduced to describe the type of scattering that does occur, and it is defined by... 

Thus, for Knudsen cosine scattering, / = 1, and for specular reflection, / = 0. Equation (59) may be solved for the drift velocity of the scattered molecule to give Uf = (1 - f)ut. The viscous force transmitted to the wall during gas collisions is the product of the number of collisions per second and the momentum change per collision,... 

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) is used to obtain spectra of powders and rough polymeric surfaces such as textiles and paper. IR radiation is focused onto the surface of the sample in a cup resulting in both specular reflectance (which directly reflects off the surface having equal angles of incidence and reflectance) and diffuse reflectance (which penetrates into the sample subsequently scattering in all angles). Special mirrors allow the specular reflectance to be minimized. 

In common with CdSe deposition from selenosulphate baths, cluster deposition of PbSe normally resulted in specular films, while ion-by-ion films were initially highly scattering as thin films but eventually (usually) became specularly reflecting with increase in thickness. As for CdSe, the development of specularity with thickness of ion-by-ion films could be explained by filling in of voids between the large crystals. 

Thin films of block copolymer melts, and block copolymers adsorbed at the liquid-liquid interface, have been investigated using specular reflectivity (largely neutron reflectivity due to the ability to vary the scattering contrast). Off-specular reflection is, in principle, a powerful method for determining in-plane structure in block copolymer films but is not yet widely used. 

Let us study some more examples of this statement. When we look at a flat object that scatters light, such as a page in a book, it appears more and more mirror-like the more we tilt it, so that we look almost parallel to the surface. The reason is that, to see a surface, that surface must have a microscopic structure whose hills and valleys must be of a size comparable at least to the wavelength of light. If the structure is finer, we do not see the surface itself instead, we see a mirror reflection, or, as it is also termed, a specular reflection. As we tilt the surface, the k value increases which produces the same result as if there had been an increase in the wavelength of the light, which is the same as a redshift. 

How are the Laue condition and the Bragg condition connected In Fig. A.3 the wave vectors of the incident and outgoing radiation and the scattering vector are drawn for the Bragg reflection of Fig. A.l. We can conclude that for specular reflection, the scattering vector lattice plane. Its length is given by... 

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