24 



CONSTRUCTION OF THE MICROSCOPE. 



In like manner, a concavo-convex lens, fig. 11, ll\ whose 

 concave surface I a I' is a circle described round the farther 



Fig. 11. 



focus of the ellipse, will cause parallel rays b I, b l f , to 

 diverge in directions I r, I 1 V, which, when continued back- 

 wards, will meet exactly in the focus/ which will be its 

 virtual focus. 



If a plano-convex lens, fig. 12, has its convex surface 

 I a l f part of a hyperboloid, formed by the revolution of a 



Fig. 12. 



hyperbola whose greater axis is to the distance between 

 the foci as unity is to the index of refraction, then parallel 

 rays rl, r" I 1 falling perpendicularly on the plane surface, 

 will be refracted without aberration to the further focus 

 of the hyperboloid. The same property belongs to a 

 plano-concave lens having a similar hyperbolic surface, and 

 receiving parallel rays on its plane surface. 1 



(1) It must be borne in mind, that in none of those lenses would the object 

 be correctly seen in focus, except at the one point known as the mathematical 

 or geometrical axis of the lens. 



