OPTICAL INSTRUMENTS. 



27 



(43.) The achromatic or negative 

 eye-piece generally adapted to astrono- 

 mical telescopes, is a combination of 

 lenses intended to correct the dispersion 

 produced by the eye-glass, independent 

 of the object lens. Let O, Fig. 28, be 



the object-glass of a telescope free from 

 chromatic dispersion, and E the eye- 

 glass ; let F be the focus of the object- 

 glass O, where an inverted image is 

 formed. Now the pencil of white light 

 A a b, when transmitted by the lens E, 



Fig. 28. 



will be divided into its component co- 

 lours, so that b R will be the direction 

 of the red rays, and b V the path of the 

 violet, and the angle V b R in crown- 

 glass will be oV f a b R. The rays 

 B a d passing through a part of the lens 

 whose surfaces are less inclined to each 

 other, will be less refracted and less 

 dispersed in the same proportion nearly, 

 and d I will be the path of the red rays, 

 and dv of the violet ; therefore, the two 

 violet rays will be very nearly parallel 



when the two red rays are rendered 

 parallel. Hence it must happen, as 

 coloured rays do not unite at the bottom 

 of the eye, that the object will appear 

 bordered with coloured fringes, and a 

 black line seen near the margin on a 

 white ground will have a ruddy and 

 orange border on the outside, and a 

 blue border within, and this confusion 

 will increase nearly in the same pro- 

 portion as the visual angle b I c. 



(44.) Fig. 29, is a section of the 

 achromatic eye-piece. Let A B be a 

 compounded pencil of white light pro- 

 ceeding from the object glass, B F a 

 plano-convex field glass, with the plane 

 side next the eye-glass E. Now the 

 red rays of the pencil A B after refrac- 

 tion would cross the axis in R, and the 

 violet rays in V, but meeting the eye- 

 glass E, the red rays will be refracted 

 to c r, and the violet to c v, when they 

 will cross one another, in the axis at 

 the point c and unite ; for the violet ray 

 being nearer the axis of the lens E, 

 will suifer less refraction than the red, 

 and when the eye is placed in the axis 

 ate, the object will appear colourless. 

 The distance of the two lenses F E, to 

 produce this correction, when made of 



crown glass, whose dispersion is as 77 to 

 78, when the incidence is 50, must be 

 equal to half the sum of their focal dis- 

 tances nearly ; or, more exactly, the 

 distance between the two lenses must 

 be equal to half the sum of the focal 

 distance of the eye-glass, and the dis- 

 tance at which the field-glass would 

 form an image of the object-glass ; for 

 the point R is the focus to which a ray 

 coming from the centre of the object- 

 glass is refracted by the field-glass, con- 

 sequently, this distance must be varied 

 according to the distance of the objects, 

 and also, as the length of the object- 

 glass ; for the same combination will 

 not be correct for a long and a short 

 object-glass, nor for celestial and ter- 

 restrial observations ; for, when it is 



