OPTICAL INSTRUMENTS. 



23 



Having thus got the radii correspond- 

 ing to the actual refractions, for the two 

 dispersive ratios 0.55 and 0.60, it only 



For 0.600 

 For 0.550 



Diff. + 0.050 



We then say as 0.050 : 0.5670.550 

 = 0.017:; -0.0064 : 0.0022 and 0.50 



: .017:: -0.3151 : -0.1071, so that 



6.6810-0.0022 and 13.8300 -0.1071 ; 

 or 6.6788 and 13.7229 are the true radii 

 corresponding to the given data : 



Thus we have in the crown lens : 



Focal length =4.3300) 



Radius of first surface = 6.6788 > 

 Index of Refraction = 1.519o) 

 From which data it is easy to com- 

 pute, by rules familiar to every optician, 

 the radius of the other surface, which 



remains to determine their values for 

 the intermediate ratio 0.567 by propor- 

 tional parts thus : 



1st radius. 



6.6746 



6.6810 



4th radius. 



13.5149 



JL3.8300 



-0.3151 



will come out, 3.3868. Again in the 

 flint lens we have for the 



Focal length = 7.635 



Radius of first surface = 13.7229 

 Index of refraction = 1.589 



Whence we find 3.3871 for the radius 

 of the other surface. 



The four radii are thus obtained 

 for a focal length of 1 inches ; and 

 to obtain them "for 30 inches we have 

 only to multiply them by 3, and we 

 obtain finally. In the case proposed, 

 the 



Radius of 1st surface, of 2nd, 3rd. 4th. 



20.0364 inches, 10.1604 inches, 10.1613 and 41.1687. 



So that here the radii of the two ad- 

 jacent surfaces scarcely differ more 

 than T^ooth of an inch, and may of 

 course be cemented together, should it 

 be thought desirable. 



(36.) The triple object-glass is con- 

 structed in the same manner as the 

 double, but as we have two convex 

 lenses to produce the required refrac- 

 tion, the total spherical aberration will 

 be less in a triple lens than in a double 

 one, and, therefore, requires less correc- 

 tion by the flint ; while the secondary 

 spectrum may be greatly diminished by 

 making one convex lens of crown, and 

 the other of Bohemia, or Dutch plate 

 glass. The theorems for finding the 

 proportionate foci of the two lenses are 

 indeterminate ; for theoretically, it is im- 

 material whether their foci be equal, or 

 in any other proportion, provided the 

 compound lens be in the ratio of the 

 dispersion of the flint. Again, the radii 

 of the concave may be varied to any 

 convenient curvature, as there are two 

 convex lenses, and, therefore, the aber- 

 ration cannot be greater than the con- 

 vex lenses will correct*. When the 

 radius of each surface is equal, and the 

 ratio of dispersion and refraction is the 



* In a double achromatic object glass, the convex 

 lens should be assumed tirst, as the flint might be 

 formed with more aberration than the convex could 

 correct. 



same as in the double achromatic object- 

 glass, and the compound focus of the 

 lens is 30 inches, the radii of the first 

 convex 



21.35. 

 .93. 



will be 



fr = 21. 

 1R = 15. 



of the concave 



second convex 



fr" 

 -j R ,, 



= 21.35. 

 15 g3 



(37.) The largest triple achromatic 

 telescope ever constructed, has lately 

 been erected in the observatory of the 

 imperial university at Dorpat, on the 

 I Oth of November, 1824, and was made 

 by Fraunhofer, the late director of the 

 Optical Institute, at Benedictbauern, 

 near Munich. 



The concave is formed from a piece 

 of dense flint glass made by Guinand, 

 and has a greater dispersive power than 

 any obtained before. It is perfectly 

 free from veins ; and the diameter of 

 the object-glass exceeds that of any 

 other telescope, having a clear aperture 

 of 9 T 6 o inches, and a focal distance of 

 25 feet. This instrument is mounted on 

 a metal stand, and although of the im- 

 mense weight of 5000 Russian pounds, 

 is moveable in every direction with the 

 slightest exertion, all the moveable parts 

 being balanced by counter- weights. It 

 has 4 eye-glasses, the lowest magnifying 



