Critical angle, determination

As for the measurement of the interfacial concentration directly, the total internal reflection fluorescence (TIRF) measurements is an effective method. Total internal reflection of condition is attained by adjusting the incident angle of the excitation beam so as to exceed the critical angle determined from the refractive indices of both phases. The penetration depth, d, is determined by... 

In Total Reflection X-Ray Fluorescence Analysis (TXRF), the sutface of a solid specimen is exposed to an X-ray beam in grazing geometry. The angle of incidence is kept below the critical angle for total reflection, which is determined by the electron density in the specimen surface layer, and is on the order of mrad. With total reflection, only a few nm of the surface layer are penetrated by the X rays, and the surface is excited to emit characteristic X-ray fluorescence radiation. The energy spectrum recorded by the detector contains quantitative information about the elemental composition and, especially, the trace impurity content of the surface, e.g., semiconductor wafers. TXRF requires a specular surface of the specimen with regard to the primary X-ray light. 

Fig. 4.11. Characteristic intensity profiles for three different kinds of concentration (a) bulk type (b) particulate type and (c) thin-layer type. The critical angle d>c is determined by total reflection at the substrate ([4.21], after Ref [4.44]).

Increase Adhesion Tension Maximize Surface Tension Minimize Contact Angle Determine the critical surfactant concentration to maximize adhesion tension. Control impurity levels in particle formation... 

The maximum input acceptance angle for a fiber-optic cable is determined by the critical angle for total internal reflection, which is given by Snell s law ... 

TXRF can be used to determine the contamination present on, in, and below the wafer surface (see Fig. 16). Changing the angle of incidence, while remaining below the critical angle of incidence, reveals the nature of the... 

Equation (11.126) shows that the critical angle coc relating base vectors Rx, R2 to eigenvectors Ui, u2 at (TC,PC) is determined by the ratio of geometrical and arithmetic means of the diagonal metric elements. Inserting the specific metric expressions from Table 11.1, we obtain finally... 

Refractometry can be used to determine the composition of a copolymer. In addition, differential refractometry has been used to study micellization in dilute block copolymer solutions (Tfizar and Kratochvfl 1972). The refractive index (n) is obtained in an Abbe refractometer via measurements of the critical angle for external reflection. The refractive index increment dn/dc, where c is the polymer concentration, can be related to the molecular weight of particles in solution. Further details of the method are provided by Pepper and Samuels (1989). 

Fig. 3.8. The analysis point. Alignment between the illuminating beam and fluid stream is critical in determining the characteristics of the resulting forward- and right-angle signals.

Let us expose an empty aquarium to rain. The vessel will fill up and water will overflow laterally toward the bases of drainage. The observation that the water is flowing indicates that the water surface, or water table, is slightly inclined (Fig. 2.12) by the critical angle of flow. This angle is determined by properties of the water, mainly viscosity, which in turn is determined by salinity and temperature. If the vessel is exposed long enough... 

A closer look at the zone of lateral base flow (overflow). Overflowing water flows laterally by the critical angle. This angle is determined by the water viscosity, which in turn is dependent on the temperature and concentration of dissolved ions. Groundwater flows laterally toward the terminal base of drainage at a critical angle that is determined by the hydraulic conductivity, or permeability, of the rocks (k) the water viscosity, which depends on the temperature (7), and the concentration of dissolved ions (i) ... 

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