F = R3/2 = focal length for paraxial rays striking an optic of curvature radius R3, D = 2xi = aperture of optical system. We may define (15) as "The fundamental expression of liquid space optics," equally useful for analysis and synthesis. From (15) note that, as you would expect, the error 5 imposed by the net axial acceleration, is inversely proportional to both liquid-vapor surface tension and fino. V, where telescopes with large f/no's already have relatively flat primaries. Hence they are going to be, if liquid, less susceptible to net axial acceleration, which is felt merely as a flattening influence anyway. Note also from (15), the error 8 will be directly proportional to net axial acceleration, ngo, and not surprisingly will also be proportional to the third power of the liquid space optical system's primary diameter. Distributing signs (removing parentheses) in Equation (8) and going back to Figure 34, note that flattening at the circumference of liquid optic under a net downward acceleration, is reflected by positive quantity 81 = zo(xi) - zbo(xi) , whereas concomitant flattening at the vertex of the liquid optic under the same net downward acceleration, is reflected by positive quantity, 82 = zbo(O) - zo(O) , such that, finally, combining (summing):
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