OONSTRUCTION OF THE MICROSCOPE. 25 



When the convex side of a plano-convex lens is exposed 

 to parallel rays, the distance of the focus from the plane 

 side will be equal to twice the radius of its convex surface 

 diminished by two-thirds of the thickness of the lens ; 

 but when the plane is exposed to parallel rays, the distance 

 of the focus from the convex side will be equal to twice 

 the radius. 



A meniscus with spherical surfaces, fig. 13, has the 

 property of refracting all converging rays to its focus, if 



Fig. 13. 



its first surface be convex, provided the distance of the 

 point of convergence or divergence from the centre of the 

 first surface is to the radius of the first surface as the index 

 of lefraction is to unity. Thus, if m ^ Z' n be a meni- 

 scus, and r I, r^ V rays converging to the point e, whose 

 distance e c from the centre of the first surface I a I' of the 

 meniscus is to the radius ca, or c I, as the index of refrac- 

 tion is to unity, that is as 1-500 to 1 in glass; then if/ is 

 the focus of the first surface, describe, with any radius less 

 than f a, a. circle m a' n for the second surface of the ieus. 

 Now it will be found by projection, that the rays r I, r V, 

 whether near the axis a e or remote from it, will be re- 

 fracted accurately to the focus/; and as all these rays fall 

 perpendicularly on the second surface m n, they will still 

 pass on, without refraction, to the focus/ In like man- 

 ner, it is obvious that rays/Z,/Z', diverging from /will 



