With the prism just considered, placed so that a vertical section is represented by a =V=, a ray is thrown upwards; if another similar prism be placed with its base in contact with the base of the other, and its apex upwards, so that its section will be represented by a =V= reversed, =Ʌ=, it is clear this will turn the rays downwards, so that the rays, on emerging from both prisms will tend to meet each other, as shown, in Fig. 22, where one ray is turned down to the same extent that the other is turned up; so that by the combination of two prisms the two rays are brought to a point, which is called a _focus_. Now, if instead of putting the prisms base to base, they are put apex to apex, a contrary action takes place, and by this means one is able to cause two rays of light to diverge instead of converging, so that the prisms, placed apex to apex, cause the rays to diverge, and when placed base to base they cause the light to converge. [Illustration: FIG. 22.—Convergence of Light by Two Prisms Base to Base. ] If instead of having two prisms merely, there be taken a system having different angles at their apices, and from each prism there be cut a section, beginning by cutting off the apex of the most powerful prism, a slice from below the apex of the next, and a slice below the corresponding part of the next, and so on; and then if these slices be laid on each other so as to form a compound prism, and another similar prism be placed with its base to this one, we get what is represented in Fig. 23. These different slices of prisms become more and more prismatic, that is, they form parts of prisms of greater angle, as they approach the ends. We can imagine a section of such a system as thin as we please. Suppose we had such a section and put it in a lathe, rotating it on the axis A B, we should describe a solid figure, and if we suppose all the angles rounded off, so that it is made thinner and thinner as we recede from the centre, the prism system is turned into a lens having the form represented in Fig. 24. In a similar manner, lenses thinner in the middle than at the edges, called concave lenses, can he constructed, some forms of which are represented in section in Fig. 25. It is also obvious that convex lenses of all curves and combinations of curves can be made, some of which appear in Fig. 26. [Illustration: FIG. 23.—Formation of a Lens from Sections of Prisms. ] [Illustration: FIG. 24.—Front View and Section of a Double Convex Lens. ] [Illustration: FIG. 25.—Double Concave, Plane Concave, and Concavo-Convex Lenses. ]