OS 



OPTICAL PRINCIPLES OF THE MICROSCOPE. 



to be at the distance of its radius, that is, in its centre of curva- 

 ture, and that of a plano-convex lens to he at the distance of twice 

 its radius, that is, at the other end of the diameter of its sphere of 

 curvature. 



5. It is evident from what has preceded, that as a double-con- 

 vex lens brings parallel rays to a focus in its centre of curvature, 

 it will on the other hand cause those rays to assume a parallel 

 direction, which are diverging from that centre before they im- 

 pinge upon it (Fig. 2) ; so that, if a luminous body be placed in the 

 principal focus of a double-convex lens, its divergent rays, falling 

 on one surface of the lens as a cone, will pass forth from its other 

 side as a cylinder. Again, if rays already converging fall upon a 

 double-convex lens, they will be brought together at a point 

 nearer to it than its centre of curvature (Fig. 3) ; whilst, if the 

 incident rays be diverging from a distant point, their focus will 

 be more distant from the lens than its principal focus (Fig. 4). 



FIG. 3. 



FIG. 4. 



Rays already converging, brought to- 

 gether at a point nearer than the principal 

 focus ; and rays diverging from a point 

 within the principal focus, still diverging, 

 though in a diminished degree. 



Rays diverging from points more distant than the 

 principal focus on either side, brought to a focus be- 

 yond it; if the point of divergence be within the circle 

 of curvature, the focus of convergence will be beyond 

 it ; and vice versa. 



The further from the point from which they diverge, the more 

 nearly will the rays approach the parallel direction; until, at 

 length, when the object is very distant, its rays in effect become 

 parallel, and are brought together in the principal focus. If the 

 rays which fall upon a double-convex lens, be diverging from the 

 farther extremity of the diameter of its sphere of curvature, they 

 will be brought to a focus at an equal distance on the other side 

 of the lens ; but the more the point of divergence is approximated 

 to the centre or principal focus, the further removed on the other 

 side will be the point of convergence, until, the point of diver- 



fence being at the centre, there is no convergence at all, the rays 

 eing merely rendered parallel. If the point of divergence be 

 within the principal focus, they will neither be brought to con- 

 verge nor be rendered parallel, but will diverge in a diminished 

 degree (Fig. 3). The same principles apply equally to a plano- 

 convex lens; allowance being made for the double distance of its 

 principal focus. They also apply to a lens whose surfaces have 



