THE MICROSCOPE AND ITS REVELATIONS. 



Parallel rays, falling on a plano-convex lens of 

 glass, brought to a focus at the distance of the 

 diameter of its sphere of curvature; and con- 

 versely, rays diverging from that point, ren- 

 dered parallel. 



still more. This will be readily comprehended when it is borne in mind 

 that the contrary direction of the second surface, and the contrary direc- 

 tion of its refraction (this being from the denser medium instead of into 



i fc )> antagonize each other; so 

 that the second convex surface 

 exerts an influence on the course 

 of the rays passing through it, 

 which is almost exactly equiva- 

 lent to that of the first. Hence 

 the focus of SL double-convex lens 

 will be at just half the distance, 

 or (as commonly expressed) will 

 be half the length of the focus 

 of a plano-convex, lens having 

 the same curvature on one side 

 (Fig. 3). 



4. The distance of the Focus 

 from the spherical surface will 

 depend not merely upon its de- 

 gree of curvature, out also upon the refracting power of the substance 

 of which it may be formed; since the lower the index of refraction, the 

 FIG. 3. less will the oblique rays be de- 



flected towards the axial ray, and 

 the more remote will be their point 

 of meeting; and conversely, the 

 greater the refractive index, the 

 more will the oblique rays be de- 

 flected towards the axial ray, and 

 the nearer will be their point of 

 convergence. A lens made of any 

 substance whose index of refrac- 

 tion is 1.5, will bring parallel rays 

 to a focus at the distance of its 

 diameter of curvature, after they 

 have passed through one convex 

 surface (Fig. 2), and at the dis- 

 tance of its radius of curvature, 

 after they have passed through 

 two convex surfaces (Fig. 3); and as this ratio almost exactly expresses 

 the refractive power of ordinary crown or plate Glass, we may for all 

 practical purposes consider the ' principal focus ' (as the focus for parallel 

 rays is termed) of a double-convex lens to be at the distance of its radius, 

 that is, in the centre of curvature, and that of & plano-convex, lens to be 

 at the distance of twice its radius, that is, at the other end of the diame- 

 ter of its sphere of curvature. 



5. It is evident from what has preceded, that as a Double-convex lens 

 brings parallel rays to a focus in its centre of curvature, it will on the 

 other hand cause those rays which are diverging from that centre before 

 they impinge upon it, to assume a parallel direction (Fig. 3); 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. If, however, 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 



Parallel rays, falling on a double-convex lens, 

 brought to a focus in the centre of its sphere of 

 curvature: conversely, rays diverging from that 

 point rendered parallel. 



