Lesson 5: Image Formation by
Lenses
The Anatomy of a Lens
If a piece of glass or other transparent material takes
on the appropriate shape, it will be capable of taking
parallel rays of incident light and either converging them
to a point or appear to diverge them from a point. Such a
piece of glass is referred to as a lens.
A lens
is merely a carefully ground or molded piece of transparent
material which refracts light rays in such as way as to form
an image. Lenses can be thought of as a series of tiny
refracting lenses, each of which refracts light to produce
their own image. When these prisms act together, they
produce a bright enough image focused at a point.
There are a variety of types of lenses.
Lenses differ from one another in terms of their shape and
the materials from which they are made. Our focus will be
upon lenses which are symmetrical across their horizontal
axis - known as the principal
axis. In this unit, we will categorize lenses as
converging lenses and diverging lenses. A
converging lens is a
lens which converges rays of light which are traveling
parallel to its principal axis. Converging lenses can be
identified by their shape; they are thicker across their
middle and thinner at their upper and lower edges. A
diverging lens is a lens
which diverges rays of light which are traveling parallel to
its principal axis. Diverging lenses can also be identified
by their shape; they are thinner across their middle and
thicker at their upper and lower edges.
A
double convex lens is
symmetrical across both its horizontal and vertical axis.
Each of the lens' two faces can be thought of as originally
being part of a sphere. The fact that a double convex lens
is thicker across its middle is an indicator that it will
converge rays of light which travel parallel to its
principal axis. A double convex lens is a converging lens. A
double concave lens is
also symmetrical across both its horizontal and vertical
axis. The two faces of a double concave lens can be thought
of as originally being part of a sphere. The fact that a
double concave lens is thinner across its middle is an
indicator that it will diverge rays of light which travel
parallel to its principal axis. A double concave lens is a
diverging lens. These two types of lenses - a double convex
and a double concave lens will be the only types of lenses
which will be discussed at The Physics Classroom.
As we begin to discuss
the refraction of light rays and the formation of images by
these two types of lenses, we will need to use a variety of
terms. Many of these terms should be familiar to you because
they have already been discussed during Unit
13. If you are uncertain of the meaning of the terms,
should spend some time reviewing them so that their meaning
is firmly internalized in your mind. They will be essential
as we proceed through Lesson 5. These terms describe the
various parts of a lens and include such words as
Principal
axis
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Vertical
Plane
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Focal
Point
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Focal
Length
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If a symmetrical lens is thought of as
being a slice of a sphere, then there would be a line
passing through the center of the sphere and attaching to
the mirror in the exact center of the lens. This imaginary
line is known as the principal
axis. A lens also has an imaginary
vertical axis which
bisects the symmetrical lens in two. As mentioned above,
light rays incident towards either face of the lens and
traveling parallel to the principal axis will either
converge or diverge. If the light rays converge (as in a
converging lens), then they will converge to a point. This
point is known as the focal
point of the converging lens. If the light rays
diverge(as in a diverging lens), then the diverging rays can
be traced backwards until they intersect at a point. This
point is known as the focal
point of a diverging lens.
The focal point is denoted by the letter
F on the diagrams below.
Note that each lens has two focal points - one on each side
of the lens. Unlike mirrors, lenses can allow light to pass
through either face, depending on where the incident rays
are coming from. Subsequently, every lens has two possible
focal points. The distance from the mirror to the focal
point is known as the focal
length (abbreviated by
"f"). Technically, a
lens does not have a center of curvature (at least not one
which has any importance to our discussion). However a lens
does have an imaginary point which we refer to as the
2F point. This is the
point on the principal axis which is twice as far from the
vertical axis as the focal point is.
As we discuss the characteristics of images produced by
converging and diverging lenses, these vocabulary terms will
become increasingly important. Remember that this page is
here and refer to it as often as needed.
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