CONSTRUCTION OF THE MICROSCOPE. 



19 



refraction at the circular surface. Hence it should follow, that a me- 

 niscus whose concave surface is part of an ellipsoid, and whose con- 

 vex surface is part of any spherical surface whose centre is in the 

 farther focus, will have no spherical aberration, and will refract pa- 

 rallel rays incident on its convex surface to the farther focus. 



In like manner, a con- 

 cavo-convex lens, fig. 11, 

 II' } whose concave surface 

 I a I' is -a eircte described 

 round the farther focus of 

 the ellipse, will cause paral- 

 lel rays b I, b' I' to diverge in 

 directions Ir, I'r", which, 

 when continued backwards, 

 will meet exactly in the fo- 

 cus jfj which will be its vir- fig. 11. 

 tual focus. 



If a plano-convex lens, fig. 12, has its convex surface I a I' part of a 

 hyperboloid, formed by the revolu- 

 tion of a hyperbola whose greater 

 axis is to the distance between 

 the foci as unity is to the index 

 of refraction, then parallel rays 

 r I, r" I' falling perpendicularly in 

 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 in its plane surface.* 



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 its first surface is con- 



* It should be borne in mind, that in none of these lenses would the object be cor- 

 rectly seen in focus, except at the one point known as the mathematical or geometrical 

 axis of the lens. 



fig. 12. 



