113.  The Shape and Material of a Lens.  The main or principal focus of a lens, that is, the point at which rays parallel to the base line AB meet (Fig. 71), depends upon the shape of the lens.  For example, a thick lens, such as A (Fig. 72), focuses the rays very near to the lens; B, which is not so thick, focuses the rays at a greater distance from the lens; and C, which is a very thin lens, focuses the rays at a considerable distance from the lens.  The distance of the principal focus from the lens is called the focal length of the lens, and from the diagrams we see that the more convex the lens, the shorter the focal length.

[Illustration:  FIG. 72.—­The more curved the lens, the shorter the focal length, and the nearer the focus is to the lens.]

The position of the principal focus depends not only on the shape of the lens, but also on the refractive power of the material composing the lens.  A lens made of ice would not deviate the rays of light so much as a lens of similar shape composed of glass.  The greater the refractive power of the lens, the greater the bending, and the nearer the principal focus to the lens.

There are many different kinds of glass, and each kind of glass refracts the light differently.  Flint glass contains lead; the lead makes the glass dense, and gives it great refractive power, enabling it to bend and separate light in all directions.  Cut glass and toilet articles are made of flint glass because of the brilliant effects caused by its great refractive power, and imitation gems are commonly nothing more than polished flint glass.

114.  How Lenses Form Images.  Suppose we place an arrow, A, in front of a convex lens (Fig. 73).  The ray AC, parallel to the principal axis, will pass through the lens and emerge as DE.  The ray is always bent toward the thick portion of the lens, both at its entrance into the lens and its emergence from the lens.

[Illustration:  FIG. 73.—­The image is larger than the object.  By means of a lens, a watchmaker gets an enlarged image of the dust which clogs the wheels of his watch.]

In Section 105, we saw that two rays determine the position of any point of our image; hence in order to locate the image of the top of the arrow, we need to consider but one more ray from the top of the object.  The most convenient ray to choose would be one passing through O, the optical center of the lens, because such a ray passes through the lens unchanged in direction, as is clear from Figure 74.  The point where AC and AO meet after refraction will be the position of the top of the arrow.  Similarly it can be shown that the center of the arrow will be at the point T, and we see that the image is larger than the object.  This can be easily proved experimentally.  Let a convex lens be placed near a candle (Fig. 75); move a paper screen back and forth behind the lens; for some position of the screen a clear, enlarged image of the candle will be made.