30 



THE MICROSCOPE. 



this fact was made by Descartes, who mathematically 

 demonstrated it. 



If a I, a I', for example, fig. 15, be part of an ellipse 

 whose greater axis is to the distance between its foci 

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

 rays r I', r" I incident upon the elliptical surface V a I, 

 will be refracted by the single action of that surface 

 into lines which would meet exactly in the farther 

 focus /, if there were no second surface intervening 

 between I a I' and /. But as every useful lens must 

 have two surfaces, we have only to describe a circle 

 I of I' round f as a centre, for the second surface of the 

 lens V I. 



As all the rays refracted at the surface I a V converge 



PIG. 15. 



accurately to /, and as the circular surface I of I' is 

 perpendicular to every one of the refracted rays, all 

 these rays will go on to / without suffering any refrac- 

 tion at the circular surface. Hence it should follow, 

 that a meniscus whose convex surface is part of an 

 ellipsoid, and whose convex surface is part of any 

 spherical surface whose centre is in the farther focus, 

 will have no appreciable spherical aberration, and will 

 refract parallel rays incident on its convex surface to 

 the farther focus. 



It is almost impossible to give microscopical lenses 

 other than the spherical form. The best made convex 

 single lenses do not bring rays of light to an exact 

 focus. If a true elliptical or hyperbolic curve could be 



