Thus far in this unit, our focus has been the
reflection of light off flat surfaces and the formation
of images by reflection
off of plane mirrors. In Lessons 3 and 4 we will turn
attention to the topic of curved mirrors, and
specifically curved mirrors which have the shape of
spheres. Such mirrors are called
spherical mirrors.
The two types of spherical mirrors are shown in the
diagram on the right. Spherical mirrors can be thought of
as a portion of a sphere which was sliced away and then
silvered on one of the sides to form a reflecting
surface. Concave
mirrors were silvered on the inside of the
sphere and convex
mirrors were silvered on the outside of the
sphere. In Lesson 3 we will focus on concave mirrors and
in Lesson 4 we will focus on
convex mirrors.
Beginning a study of
spherical mirrors demands that you first become
acquainted with some terminology which will be
periodically used. The internalized understanding of the
following terms will be essential during Lessons 3 and
4.
Principal
axis
Center of
Curvature
Vertex
Focal
Point
Radius of
Curvature
Focal
Length
If a concave mirror 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 mirror. This line
is known as the principal
axis. The point in the center of sphere from
which the mirror was sliced is known as the
center of curvature
and is denoted by the letter
C in the diagram
below. The point on the mirror's surface where the
principal axis meets the mirror is known as the
vertex and is denoted
by the letter A in
the diagram below. The vertex is the geometric center of
the mirror. Midway between the vertex and the center of
curvature is a point known as the
focal point; the
focal point is denoted by the letter
F in the diagram
below. The distance from the vertex to the center of
curvature is known as the radius
of curvature (abbreviated by
"R"). The radius of
curvature is the radius of the sphere from which the
mirror was cut. Finally, the distance from the mirror to
the focal point is known as the
focal length
(abbreviated by "f").
Since the focal point is the midpoint of the line segment
adjoining the vertex and the center of curvature, the
focal length would be one-half the radius of
curvature.
The focal point is the
point in space at which light incident towards the mirror
and traveling parallel to the principal axis will meet
after reflection. The
diagram at the right depicts this principle. In fact, if
some light from the Sun was collected by a concave
mirror, then it would converge at the focal point.
Because the Sun is such a large distance from the Earth,
any light rays from the Sun which strike the mirror will
essentially be traveling parallel to the principal axis.
As such, this light should reflect through the focal
point. Perhaps you remember the outdoors demonstration in
which a pencil was engulfed in flames in a matter of
seconds when placed at the focal point of the
demonstration mirror. In the demonstration, whatever
light from the Sun which hit the mirror was focused at
the point where the pencil was. To the surprise of many,
the heat was sufficient to ignite the pencil. Wow!
As we proceed through Lesson 3, we will
observe the images formed by concave mirrors. Depending
on the object location, the image could be enlarged or
reduced in size or even the same size as the object; the
image could be inverted or upright; and the image will be
located in a specific region along the principal axis. To
understand these relationships between object and image,
you may need to review these vocabulary terms.
Check
Your Understanding
Light from a distant star is collected by a
concave mirror. How far from the mirror do the light
rays converge if the "radius of curvature" of the
mirror is 150 cm?
Suppose your teacher gives you a concave mirror
and asks you to find the focal point. Describe the
procedure you would use to do this.
