Concave Mirrors
The Anatomy of a Curved Mirror
Thus far in this unit, our focus has been the reflection
of light off flat surfaces and the formation of images by
plane mirrors. In Lessons 3 and 4 we will turn our attention
to the topic of curved 
mirrors,
and specifically curved mirrors which have a
spherical shape. 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.
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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 the 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 (represented 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 (represented 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 and pass through the focal point. A
common Physics demonstration involves using a large
demonstration mirror to set a pencil aflame in a matter of
seconds. In the demonstration, the pencil is placed at the
focal point and the concave mirror is pointed upwards
towards the sun. Whatever rays of light from the sun which
hit the mirror are focused at the point where the pencil is
located. To the surprise of many, the heat is 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 the vocabulary terms described on this page.
Check Your
Understanding
1. The surface of a concave mirror is pointed towards the sun. Light from the sun hits the mirror and converges to a point. How far is this converging point from the mirror's surface if the radius of curvature (R) of the mirror is 150 cm?
2. It's the early stages of a concave mirror lab. Your teacher hands your lab group a concave mirror and asks you to find the focal point. What procedure would you use to do this?