6 THE MICROSCOPE AND ITS REVELATIONS. 



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

 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 negative focus will ap- 

 proach 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 be- 

 tween 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 either on a 

 ' bundle ' of parallel rays, or on 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 com- 

 prehending an infinite number of such points, from every one of which a 

 pencils of rays proceeds, to be refracted in its passage through a lens 

 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 distance of the princi- 

 pal focus, the image, being formed at an equal distance on the other side 

 of the lens ( 5), will be of the same dimensions with the object : whilst, 

 on the other hand, if the object (Fig. 7, a b) be nearer the lens, the 



j,, IO 7 image A B will be farther from 



it, and of larger dimensions; 

 but if the object A B be farther 

 from the lens, the image a b 

 will be nearer to it, and smaller 

 than itself. Further, it is to 

 be remarked that the larger 

 the image in proportion to 

 the object, the less bright will 

 it be, beca'use the same amount 

 of light has to be spread over 

 a greater surface; whilst an 



Formation of Images by Convex Lenses. imag? that ig smaller than the 



object will be more brilliant in the same proportion. 



9. A knowledge of these general facts will enable the learner to un- 

 derstand the ordinary action of the Microscope; but the instrument is 

 subject to certain optical imperfections, the mode of remedying which 

 cannot be comprehended without an acquaintance with their nature. One 

 of these imperfections results from the unequal refraction of the rays 



