8 OPTICAL PRINCIPLES OF THE MICROSCOPE. 



verging fall upon a double-convex lens, they -will be brought toge- 

 ther at a point nearer to it than its centre of curvature (Fig. 6). — 

 The same principles apply equally to a Plano-convex lens ; allow- 

 ance being made for the double distance of its principal focus. 

 They also apply to a lens whose surfaces have different curvatures ; 

 the principal focus of such a lens being found by multiplying the 

 radius of one surface by the radius of the other, and dividing this 

 product by half the sum of the same radii. — The rules by which 

 the foci of convex lenses may be found, for rays of different 

 degrees of convergence and divergence, will be found in works on 

 Optics. 



6. The refracting influence of concave Lenses will evidently be 

 precisely the opposite of that of convex. Rays which fall upon 

 them in a parallel direction, will be made to diverge as if from 

 the principal focus, which is here called the negative focus. This 

 will be, for a plano-concave lens, at the distance of the diameter of 

 the sphere of curvature ; and for a double-concave, in the centre 

 of that sphere. In the same manner, rays which are converging 

 to such a degree, that, if uninterrupted, they would have met in 

 the principal focus, will be rendered parallel ; if converging more, 

 they will still meet, but at a greater distance ; and if converging 

 less, they will diverge as from a negative focus at a greater distance 

 than that for parallel rays. If already diverging, they will diverge 

 still more, as from a negative focus nearer than the principal focus ; 

 but this will approach the principal focus, in proportion as the 

 distance of the point of divergence is such that the direction of 

 the rays approaches the parallel. 



7. If a Lens be convex on one side and concave on the other, 

 forming what is called a meniscus, its effect will depend upon the 

 proportion between the two curvatures. If they are equal, as in a 

 Watch-Glass, scarcely any perceptible effect will be produced ; if the 

 Convex curvature be the greater, the effect will be that of a less 

 powerful convex lens : and if the Concave curvature be the more 

 considerable, it will be that of a less powerful concave lens. The 

 focus of convergence for parallel rays in the first case, and of 

 divergence in the second, may be found by dividing the product 

 of the two radii by half their difference. 



8. Hitherto we have considered only the effects of Lenses upon 

 a ' pencil' of rays issuing from a single luminous point, and that 

 point situated in the line of its axis. If the point be situated 

 above the line of its axis, the focus will be below it, and vice versa. 

 The surface of every luminous body may be regarded as compre- 

 hending an infinite number of such points, from every one of 

 which a pencil of rays proceeds, and is refracted according to the 

 laws already specified ; so that a complete but inverted Image or 

 picture of the object is formed upon any surface placed in the 

 Focus and adapted to receive the rays. It will be evident from 

 what has gone before, that if the object be placed at twice the 



