If the reflecting surface be concave, as in Pl. XII. fig. 4, parallel rays will be reflected to a focus _a_, nearer the mirror than the centre of its curvature _b_, and this focus is called the principal focus; while diverging rays are brought to a focus nearer the centre of curvature; and converging rays form a focus further from the centre of curvature. _Lenses._--In most instances, as far as the microscope is concerned, the surfaces of the glass through which the rays of light are transmitted are not plane or flat, but curved-being either convex or concave, and belonging to convex or concave lenses. In considering the course of rays through curved surfaces, the refraction may be viewed as taking place at a plane surface forming a tangent at the point of incidence of each ray; or each curved surface may be regarded as consisting of a number of minute plane surfaces placed at right angles to the perpendicular. Thus, in Pl. XII. fig. 5, the ray _a_, incident at the point _b_ of the curved surface, is refracted towards the perpendicular _p_, as if it had fallen upon the plane surface represented by the tangent _t_. The forms of the most common lenses are represented in Pl. XII. figs. 6-10;--fig. 6 being doubly convex, or both surfaces being convex; fig. 7, plano-convex, or one surface plane, the other convex; fig. 8, doubly concave, or both surfaces being concave; fig. 9, plano-concave, one surface being plane, the other concave; and fig. 10 is a meniscus, in which one surface is convex and the other concave. The curved surfaces of lenses are usually portions of spheres. The manner in which the course of a ray may be traced through a lens is illustrated by Pl. I. fig. 11, which requires no explanation after what has been already stated. To facilitate the comprehension of the general action of lenses, they may be regarded as composed of two triangular prisms, with their bases in contact in a convex lens, as in fig. 12; their apices being opposed in a concave lens, as in fig. 13. The point to which the rays converge after passing through a convex lens is called the _focus_ (Pl. XII. fig. 14 _f_), the distance of which from the centre of the lens, called the focal length, obviously depends upon the direction of the incident rays. When these are parallel, which those coming from distant objects may be considered to be, the focus at which they meet is called the principal focus, or the focus for parallel rays: thus, in Pl. XII. fig. 14, the parallel rays meet at _f_, which is the principal focus.