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Permissible curvature of prism surfaces and inaccuracy of collimation in precise minimum-deviation refractometry

1933; Volume: 11; Issue: 1 Linguagem: Inglês

10.6028/jres.011.005

2376-9815

L.W. Tilton,

Surface Roughness and Optical Measurements

Care in the optimum translational adjustment of a prism in order to permit the symmetrical use of all apertures is always necessary on account of aberrations inherent in lens systems.Such prism adjustments are advisable also because of slight curvatures of most prism surfaces.When prisms are at all times correctly located with respect to the axes of collimator, telescope, and spectrom- eter, the departures of the surfaces from planeness may then be appreciably greater than has hitherto been recognized as allowable.Moreover, it is shown that the latitude in collimation becomes sufficiently large to permit making all necessary refocusings with the telescope, even when using objectives with the usual type of color correction.Tolerances, corresponding to an error of ± 1 X 10~8 in index of refraction, are evaluated for curvature of prism surfaces, translational adjustment of the prism, eccentricity of prism-table axis, and collimator ref ocusing.CONTENTS Page I. Introduction 26 II.Symmetrical use of the prism and the lens systems 29 1.Lens aberration and "obliquity" errors 30 2. Methods of refracting-angle measurement and curvature of prism surfaces 30 3. Minimum-deviation measurement and curvature of prism surfaces 31 III.Relations between curvature of prism surfaces and prism-position adjustment 32 Tiiton] Prism Surface Planity and Collimation 27 c and c' = cosines of incidence angles on first and second faces of prism as oriented for minimum deviation; that is, c = cos -~-and c' =cos (A/2); D, D e , and D e = angles of minimum deviation produced, respectively, by a prism correctly placed, asymmetrically tabled, and tabled with respect to an eccentric table axis; E=\ distance through which, after refracting- angle measurement, the prism vertex should be translated toward the table axis preparatory to deviation measurement for a wave length X; e A = linear asymmetry of prism position (when making refracting-angle measurements) measured from prism-table axis to the intersection of normals erected at the surface centers of the effective isosceles portion of the prism; e D = linear asymmetry of prism position (when making minimum-deviation measure- ments) measured from prism-table axis to the intersection of the incident and emergent chief rays; e AR and Zalerrors in tabling a prism for refracting- angle measurement as measured per- pendicularly to the line of sight at the right-and left-hand telescope pointings; e DR and e DL = errors in tabling a prism for minimum- deviation measurement as measured perpendicularly to the line of sight at the right-and left-hand pointings ; e m = maximum error (measured perpendicu- larly to the telescope pointings) that is made in translational adjustment of a prism ; e= linear eccentricity of prism-table axis with respect to axis of the spectrome- ter; 77= phase difference in complete periods or cycles ; /= focal length of telescope objective; / c = focal length of collimator objective; /' c = adequate collimator focal length which permits refractive-index measurement without chromatic refocusing of colli- mator; ftP = combined focal length of telescope objec- tive and prism; F c = actual collimator tube length or distance from collimator slit to objective;