ON ACHROMATIC ETE-PIECES.
In order to correct the chromatic aberration in the eyepieces of telescopes, we are not under the necessity of using compound lenses of different dispersive powers, as all the orders of rays can be united by a particular arrangement of the eye-glasses. This will be obvious from Plate 1V. Fig. 6., where AB is a compound object glass, and DE an eyepiece, consisting of two lenses D, E. Then if CDE be the axis of the telescope, and PS a ray of white light passing through the object glass, since the object-glass is achromatic, this ray will fa.11 upon the eye-glass D, without being separated into the prismatic colours, through whatever part of the com pound lens it is transmitted. This ray, however, will be decomposed after refraction through the lens D, and the red rays will be bent into the direction SR, and the vio let into the direction SV. But these rays are intercepted by the second lens E, at the points 7a a ; and as the re fracting angle of the lens is greater at in than at n, this increase of the refracting angle for the red ray will make up for its inferior refrangibility, and the rays S m. S a, will emerge parallel from the lens in the lines no-, nv. The chromatic aberration, therefore, which is always proportional to the angle formed by the rays Mr, nv, will be destroyed.
In small telescopes and opera-glasses, where it would be very inconvenient to have a long eye-piece composed of several lenses, a compound lens of crown and flint glass should be used, and may consist either of three or two glasses, with the following curvatures ; the letters a, b, &c. representing the same. radii as before, and F the focal length of the compound lens being = I.
If the object is to be erect, as in the Galilean teles cope, the lens of flint glass must be made convex, and those of crown class concave, in order that the concavity of the compound glass may predominate.
An achromatic eye-piece for astronomical telescopes, of the same kind as that which is represented iu Fig. 6. should have the focal length ()I the lens 1) triple that of the lens E, and the distance DE should be double the focal length of E, or two-thirds of the focal length of D. In one of Dollond's best telescopes, the focal length of D was 12.75 lines, and its thickness 1.62 lines ; the focal length of E, 5.45 lines, its thickness 1.25 lines, and the distance between their interior surfaces 4.20 lines : in
another eye-piece of Dollond's construction, the focal length of D was 8.30 lines, and its thickness 1.60 : the focal length of E 3.53, and its thickness 0.97. In both these eye-pieces, the lenses should he plano-convex, with their plane sides turned to the eye, in order to di minish the spherical aberration.
When the achromatic eye-piece consists of three lenses, it may be constructed by the Mowing formula', where F is the focal length of the object-glass, and .r, zj, z, the focal length or the eye-glasses, reckoning from that which is nearest the object.
The focal length of the 3 lenses may be made equal, though it is preferable to give the third less focal length than the other two, and to make its distance from the second equal to its own focal length, added to 11, the focal length of one of the other lenses ; for un when x y, the expression y + becomes z+ 1-p. In this case the magnifying power of the eye piece is equal to that of the third lens a.
Achromatic eye-pieces may be made of four lenses, if their focal lengths arc as the numbers 14, 21, 27, 32 ; their distances 23, 44, 40; their apertures 5.6; 3.4; 13.5 ; 2.6 ; and the aperture of the field bar in the an terio• focus of the 4th eye-glass 7.
In one of Bamsden's eye-pieces of four lenses, the focal lengths were 0.77 of an inch ; 7.025; 1.01 ; 0.79 ; and their distances 1.18; 1.83; 1.10, reckoning from the lens next the object. This eye-piece was equal to a lens 0.566 inches in focal length.
In one of Dollond's best eye-pieces, the focal lengths were 1441ines ; 19; 224 ; 14; the distances 22.48 ; 46.17; 21.45, and the thickness of the lenses at their centre 1.23; 1.25 ; 1.47.
With the intention of enlarging the field of view, Mr Dollond constructed some eye-pieces, consisting of five, and some even of six lenses ; but the limits of this work will not permit us to enter into any details respecting their construction. Besides the works quoted nod A ne.a itisTioN, in °Mies, See .A/•/n. Pon. 1779, p.
3./mccIlrinca Taurincnsia, tom. 3. part iii. p. 92. Dhpirics. Roclion's Ofinscutc.s., 1768. Rochon's hop ()tics, I 783. Boscovich's ricnna, 1767. snllz Cunnochiali, 1781. And two French translations or Smith's Optics., by P&zcnas, and i1. Du la] lc lloi, 1767. See also OPTICS. (w)