CAMPANl'S EYE-PIECE. 35 



reason eye-pieces of modern Microscopes consist, as a rule, of two 

 lenses so combined that their aberrations approximately neutralize 

 each other. The combination of these lenses admits of certain 

 modifications from an optical point of view, of which we may 

 specially mention the following: 



a. The Campani (or Huygheniari) Eye-piece. 



The so-called Campani eye-piece consists of two plano-convex 

 lenses, the lower one of which is called the field-lens, the upper 

 the eye-lens. The former collects the converging rays coming 

 from the objective before they have united into an image, and 

 forms the image within the focus of the eye-lens, so that it can be 

 viewed through the latter as through a magnifying lens. 



For the mathematical consideration of the eye-piece it is 

 perfectly immaterial in what manner it is combined with the 

 objective. We may, for instance, first bring the field-lens into 

 the calculation, and then combine the eye-lens with the resulting 

 system ; or, conversely, first determine the action of the eye-piece 

 as a whole, and then its action in combination with the objective. 

 We will choose the latter. 



Let the focal lengths of the field-lens and eye-lens be respect- 

 ively 40 mm. and 30 mm., their thickness 3 mm. and 2 mm. If, 

 then, we denote the two pairs of principal points by E, P, and 

 E ', 1', and the vertices of the refracting surfaces in their order 

 from below upwards by N, N\ N 2 , N 3 , and assume the index 

 of refraction of the lenses to be 1'5, and their distance from each 

 other as 43 mm., we get 



E' = iV 2 , r = N* + ; 



o 



&> = ^V , 7 = 

 E' 



consequently 



t' = E' - 1 = 45 , 



and, hence, for the resultant principal and focal points E E*, F F*, 



E = E + 72 = N* + 24 , E* = 1' - 54 = N B - 55i, 

 F = .V 3 - 24 , F* = .V 3 + 7i, 



E - F = F* - E* 48 . 



With reference to this system of cardinal points, which repre- 

 sents the eye-piece as a whole, the image which is actually formed 



D 2 



