last three types, called concave lenses, scatter parallel rays so that
they do not come to a focus, but diverge widely after passage through
the lens.

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