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].
Fig. 23.—Formation of a Lens from Sections of Prisms.
Fig. 24.—Front View and Section of a Double Convex Lens.
Fig. 25.—Double Concave, Plane Concave, and Concavo-Convex Lenses.
The action of such lenses upon the light proceeding from any source may now be considered. If there is a parallel beam proceeding from a lamp, or from the sun, and it falls on the form of lens, called a convex lens, which bulges out in the middle, we learn from Fig. [27], that the upper part acts like the upper prism just considered and turns the light down, and the lower acts in the reverse manner and turns the light up, and the sides act in a similar manner; and as the inclination of the surfaces of the lens increases as we approach the edge, the rays falling on the parts near the edge are turned out of their course more than those falling near the centre, so that we have the rays converged to a point F, called the focus of the lens; and as the rays from an electric lamp are generally rendered parallel by means of the lenses in the lantern, called the condensers, the rays from such a lamp falling on a convex lens will come to a focus at just the same distance from the lens, called its principal focal length as they would do if they came from the sun or stars.