Caustic coordinates in Platzeck-Gaviola test of conic mirrors.
The centers of curvature of all zones of a spherical mirror coincide at the center of that sphere. In the case of all other conies of revolution, however, the radii of curvature of dif­ ferent zones have different magnitudes; hence their centers of curvature do not coincide but lie along the caustic curve, as shown by Wadsworth. Based on this property Platzeck and Gaviola devised a test to measure the shape of a para­ boloid being figured. What they do is to measure the posi­ tions of the centers of curvature of different regions in the optical surface, then the results are compared with the theo­ retical values. The theoretical positions of these centers of curvature for a paraboloid are computed with two simple formulas given by Schroader, but to our knowledge the ex­ pressions for any conic of revolution have not been given. To derive the expressions for the caustic coordinates (η,ξ) of the centers of curvature of the conic surface (see Fig. 1), we
The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface.
The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.
Effects of Equipment Dimensions on Liquid Mixing Time of Bubble Column with Draft Tube
The liquid mixing time of a bubble column with a draft tube is experimentally studied. The diameter and height of the column, the diameter and length of the draft tube, and the mode of sparging gas were changed and the liquid mixing time was measured.The lengths of bottom and top clearances have significant effects on the liquid mixing time. The liquid mixing time increases with increasing column aspect ratio of height to diameter. The liquid mixing time of the bubble column with a draft tube is longer than that of a standard bubble column when the column aspect ratio is relatively high. The liquid mixing time has a minimum when the diameter ratio of draft tube to column is 0.5 to 0.6. These effects of equipment dimensions are expressed by an equation. In the experiment using different solutions, the liquid mixing time becomes shorter with increasing liquid surface tension, or with increasing liquid viscosity.