I. OPTICAL PRINCIPLES GOVERNING TILE CONSTRUCTION OF MICROSCOPES.
All microscopes, except those which operate by reflection (to be hereafter noticed), depend for their operation upon the influence of convex and concave lenses on the course of the rays of light passing through them. This influence is the result of the well-known laws of refraction —that a ray passing from a rare into a dense medium is refracted towards the perpendicular, and vice versa. When, therefore, a pencil of parallel rays passing through air impinges upon a convex surface of glass, the rays will be made to converge, for they will be bent towards the centre of the circle, since the radius is the per pendicular to each point of curvature. The central ray, as it coincides with the perpendi cular, will undergo no refraction ; the others will be bent from their original course in an increasing degree in proportion as they fall at a distance from the centre of the lens ; and the effect upon the whole will be such, that they will be caused to meet at a point, called the jivers, some distance beyond the centre of cur vature. This effect will not be materially changed, by allowing the rays to pass into air again through a plane surface of glass, such as would be formed by a section of the glass in the vertical line; a lens of this description is called a piano-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 sur face, the rays re-enter the air through a convex surface, they will be made to converge still more. This may be best understood by considering the course of parallel rays, as in the adjoining if a double convex lens will bring parallel rays to a focus in the centre of its sphere of curva ture, it will on the other hand cause rays to assume a parallel direction, which are divcrging from its focus; so that if a luminous body were placed in that point, all its cone of rays, which fell upon the surface of the lens, would pass out in a cylindrical form. Again, if rays al ready converging fall upon a convex lens, they figure (fig. 145). Here the radii prolonged will be the perpendiculars to the curved surface; and, according to the law of refraction just alluded to, the rays passing from the dense into the rare medium will be bent from the perpendicular, so as to be made to converge towards a focus, as in the former instance. It is easy to see,
therefore, that the effect of the second convex surface will be precisely equivalent to that of the first; for the contrary direction of the sur face is antagonized by the contrary direction of the refraction ; so that the focus of a double convex lens will be at just half the distance from it, or (as commonly expressed) be half the length of the focus of a plano-convex lens. In fact, the focus of the former to parallel rays will be the centre of its sphere of curvature, and its focal length will therefore be the radius; whilst the focus of the latter will be in the op posite side of the sphere, and its focal length will be the diameter. Now it is evident that will be brought to a focus at a point nearer to it than the focus for parallel rays (which is called its principal focus); and, if they be di verging from a distant point, their focus will be more distant than the principal focus. The further be the point from which they diverge, the more nearly will the rays approach the pa rallel direction ; until, at length, when the ob jects are very distant, their rays in effect become parallel, and are brought to a focus in the centre of the sphere. If they diverge from the other extremity of the diameter of the sphere, they will be brought to a focus at a correspond ing distance on the other side of the lens. On the other hand, if they be diverging from a point within the principal focus, they will neither be brought to converge nor be rendered parallel, but will diverge in a diminished degree. The same principles apply equally to a plano convex lens, the distance of its principal focus being understood to be the diameter of the sphere. They also apply to a lens whose sur faces have different curvatures ; the principal focus of such a lens is found by multiplying the radius of one surface by the radius of the other, and dividing thisproduct by half the sum of the same radii. For the rules by which the foci of convex lenses may be found for rays of different degrees of convergence and divergence, we must refer to works on optics.