[Illustration: Fig. 8.--Converging and Diverging Lenses.]
Lenses with sharp edges (thicker at the centre) are _convergent_ or _positive_ lenses. Lenses with blunt edges (thinner at the centre) are _divergent_ or _negative_ lenses. The first group comprises:--(1) The bi-convex lens; (2) the plano-convex lens; (3) the convergent meniscus. The second group:--(4) The concave lens; (5) the plano-concave lens; (6) the divergent meniscus (Fig. 8).
=Principal Focus.=--A lens is usually a solid of revolution, and the axis of revolution is termed the principal axis of the lens. When the surfaces are spherical it is the line joining the centre of curvature.
From the great importance of lenses, especially convex lenses, in practical optics, it will be necessary to explain their properties somewhat at length.
[Illustration: Fig. 9.--Principal Focus of a Convex Lens.]
=Principal Focus of Convex Lens.=--When rays which were originally parallel to the principal axis pass through a convex lens (Fig. 9), the effect of the two refractions which they undergo, one on entering and the other on leaving the lens, is to make them all converge approximately to one point F, which is called the principal focus. The distance A F of the principal focus from the lens is called the principal focal distance, or more briefly and usually, the focal length of the lens. The radiant point and its image after refraction are known as the conjugate foci. In every lens the right line perpendicular to the two surfaces is the _axis_ of the lens. This is indicated by the line drawn through the several lenses, as seen in the diagram (Fig. 8). The point where the axis cuts the surface of the lens is termed the _verte_.
Parallel rays falling on a _double-convex_ lens are brought to a focus in the centre of its diameter; conversely, rays diverging from that point are rendered parallel. Hence the focus of a _double-convex_ lens will be at just half the distance, or half the length, of the focus of a _plano-convex_ lens having the same curvature on one side. The distance of the focus from the lens will depend as much on the degree of curvature as upon the refracting power (termed the index of refraction) of the glass of which it may be formed. A lens of crown-glass will have a longer focus than a similar one of flint-glass; since the latter has a greater refracting power than the former. For all ordinary practical purposes we may consider the _principal focus_--as the focus for parallel rays is termed--of a double-convex lens to be at the distance of its radius, that is, in its centre of curvature; and that of a plano-convex lens to be at the distance of twice its radius, that is, at the other end of the diameter of its sphere of curvature. The converse of all this occurs when divergent rays are made to fall on a convex lens. Rays already converging are brought together at a point nearer than the principal focus; whereas rays diverging from a point within the principal focus are rendered still more diverging, though in a diminished degree. Rays diverging from points more distant than the principal focus on either side, are brought to a focus beyond it: if the point of divergence be within the circle of curvature, the focus of convergence will be beyond it; and _vice-versâ_. The same principles apply equally to a _plano-convex lens_; allowance being made for the double distance of its principal focus; and also to a lens whose surfaces 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 this product by half the sum of the radii.