REFRACTION BY CONVEX LENSES. 



67 



ally changed by allowing rays to pass into air again through 

 a plane surface of glass, perpendicular to the axial ray (Fig. 1); 

 a lens of this description is called a plano-convex lens; and it 

 will hereafter be shown to possess properties, which render it 

 very useful in the construction of microscopes. But if, instead 

 of passing through a plane surface, the rays re-enter the air 

 through a second convex surface, turned in the opposite direction, 

 as in a double-convex lens, they will be made to converge still 

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

 mind that the contrary direction of the second surface, and the 



FIG. 1. 



FIG. 2. 



Parallel rays, falling on a plano-convex lens, Parallel rays, falling on a double-convex lens, 



brought to a focus at the distance of its diameter; brought to a focus in its centre ; conversely, rays 



and conversely, rays diverging from that point, diverging from that point, rendered parallel, 

 rendered parallel. 



contrary direction of its refraction (this being from the denser me- 

 dium instead of into it), antagonize each other ; so that the second 

 convex surface exerts an influence on the course of the rays pass- 

 ing through it, which is almost exactly equivalent to that of the 

 first. Hence the focus of a double-convex lens will be just half 

 the distance, or (as commonly expressed) will be at half the 

 length, of the focus of a plano-convex lens having the same cur- 

 vature on one side (Fig. 2). 



4. The distance of the focus from the lens will depend, not 

 merely upon its degree of curvature, but also upon the refracting 

 power of the substance of which it may be formed; since the 

 lower the index of refraction, the less will the oblique rays be 

 deflected 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 deflected towards the axial ray, 

 and the nearer will be their point of convergence. A lens made 

 of any substance whose index of refraction is 1-5, will bring 

 parallel rays to a focus at the distance of its diameter of curva- 

 ture, after they have passed through one convex surface (Fig. 1), 

 and at the distance of its radius of curvature, after they have 

 passed through two convex surfaces (Fig. 2) ; and as this ratio 

 almost exactly expresses the refractive power of ordinary Glass, 

 we may for all practical purposes consider the " principal focus" 

 (as the focus for parallel rays is termed), of a double-convex lens 



