Ray caustics

If we combine curvature of the ray path with the notion of the turning point, then the ray path must qualitatively look like the path in Fig. l-7(a) when Eq. (1-22) has a solution, and like Fig. l-7(b) when Eq. (1-22) has no solution. In the first case the ray path bends continuously until it returns to the axis, and in the second case it reaches the interface, where it is totally transmitted. Since the profile is assumed continuous across the interface, the angles of incidence and transmission are all equal, and 0t = 0 (p). The dashed line at x = x,p is the locus of turning points for all rays with the same value of 0 (0), and is often called the ray caustic or turning-point caustic. 

Fig. 2-8 Rectangular turning-point caustics for fibers with the separable profiles of Eq. (2-58), showing (a) a bound-ray caustic and (b) a tunneling-refracting ray caustic [5].

Selective removal of the less noble constituent has been demonstrated by chemical analysis in the case of nickel-rich alloys in fused caustic soda or fused fluorides ", and by etching effects and X-ray microanalysis for Fe-18Cr-8Ni steels in fused alkali chlorides. This type of excessive damage can occur with quite small total amounts of corrosion, and in this sense its effect on the mechanical properties of the alloy is comparable with the notorious effect of intercrystalline disintegration in the stainless steels. 

Carbon, analysis, 217, 318, 319 Carbon brushes, examination by x-ray absorptiometry, 97 Cathode follower, 60 Cauchois arrangement, 119, 120, 123 Caustic circle, 119, 120 Cells for liquids, 191, 194 Cements, analysis in Applied Research Laboratories PXQ, 260, 261 Ceramics, analysis by x-ray emission spectrography, 222-224 Cerenkov radiation, 43 Cesium, determination by x-ray emission spectrography, 328 Characteristic-line generator of Eng-strom, 144... 

Elemental composition Hg 76.39%, N 5.33%, 0 18.28%. The salt is dissolved in dilute nitric acid and analyzed for mercury (see Mercury). The compound is blackened by ammonia and caustic alkali solutions. It may be identified by physical and x-ray properties. 

Elemental composition W 79.30%, 0 20.70%. Tungsten trioxide may be identified by its physical properties or by x-ray diffraction methods. The oxide is either digested in aqua regia or dissolved in caustic alkalies, diluted, and analyzed for tungsten metal (See Tungsten). 

Since the alpha-ray impacts shattered only a minute proportion of the total number of atoms of boron, aluminum, or magnesium, the chemical identification of the products was extremely difficult. These indefatigable workers, however, accomplished even this. Although it would have been impossible to identify the products simply by ordinary chemical means, the Joliots were able to take advantage of the radioactive nature of the products formed. Since they had good reason to believe that the boron atom had captured a helion and ejected a neutron and that the new element was therefore probably an isotope of nitrogen, they heated some bombarded boron nitride with caustic soda and found that the liberated... 

In optical terms the Lagrange manifolds are the same as what Hamilton called ray systems (a system of normals to a smooth surface may serve as an example). In this case, the caustic is the point of the concentration of light. Thus, Ya.B. s pancake theory in particular predicts that the first caustics in a weakly inhomogeneous system of rays have the form of saucers (in a dispersive medium the saucers may become visible). 

CaSi2 yields siloxene via acid hydrolysis (HC1) in darkness in alcoholic solution under nitrogen. Siloxene is a white powder which is insoluble in all solvents, gives no X-ray lines, burns spontaneously in air and evolves hydrogen with caustics. The stmcture was shown above. 

Potassium osmiamate, K[Os( VIII )03N], is prepared by the addition of aqueous ammonia to a solution of osmium tetroxide, 0s04, in caustic potash solution (6). X-ray studies show the molecule to be basically... 

X-Ray Diffraction Mineralogy Caustic Consumption (meq NaOH/kg Rock) ... 

Na+-0H2 at bond distances of 2.03 A. At 38 weight percent caustic a NaOH 3.6H20 composition is found at 536 GPL (25). In these very concentrated solutions, formation of Na+OH" ion - pairs is assumed to exist. Even though it may not be generally agreed that it is justifiable to draw detailed conclusions about structures of ionic solutions from their x-ray scattering patterns, it is possible to obtain information about the structure and immediate environment of certain ions in this manner (25) (27). 

If a given system of rays be incident upon a bright curve, the envelope of the reflected rays is called a caustic by reflection. 

DISPOSAL AND STORAGE METHODS absorb with vermiculite, dry sand, or earth, and dispose in a secured sanitary landfill atomize in a suitable combustion chamber equipped with an appropriate effluent gas cleaning device store in a cool, well-ventilated place keep out of direct rays of the sun, and away from flames, sparks, active metals, strong caustics, and strong oxidizers. 

Raney nickel /ray-nee/ A catalytic form of nickel produced by treating a nickel-aluminum alloy with caustic soda. The aluminum dissolves (as aluminate) and Raney nickel is left as a spongy mass, which is pyrophoric when dry. It is used especially for catalyzing hydrogenation reactions. 

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