Answer to Essential Question 23.5: To add fractions you need to find a common denominator.
. This gives .
23-6 Analyzing the Concave Mirror
In section 23-4, we drew one ray diagram for a concave mirror. Let’s investigate the
range of ray diagrams we can draw for such a mirror.
EXPLORATION 23.6 – Ray diagrams for a concave mirror
Step 1 – Draw a ray diagram for an object located 40 cm from a concave mirror that has a
radius of curvature of 20 cm. Verify the image location on your diagram with the mirror
equation. In drawing a ray diagram, it is helpful to know where the mirror’s focal point is. For a
spherical mirror, the focal point is halfway between the mirror’s center of curvature and the point
at which the principal axis intersects the mirror. Thus, the focal length in this case is +10 cm.
In Figure 23.29, two rays are shown.
One is the parallel ray, which leaves the tip of
the object, travels parallel to the principal axis,
and reflects from the mirror so that it passes
through the focal point. The second ray reflects
off the mirror at the point at which the principal
axis meets the mirror, reflecting as if the mirror
was a vertical plane mirror.
Applying the mirror equation, in the
form of equation 23.5, to find the image
distance:
.
This image distance is consistent with the ray diagram in Figure 23.29.
Step 2 – Repeat step 1, with the object now
moved to the center of curvature. The parallel
ray follows the same path as it did Figure
23.29. As shown in Figure 23.30, the ray that
reflects from the center of the mirror follows a
different path, because shifting the object
changes the angle of incidence for that ray. This
situation is a special case. When the object is
located at the center of curvature, the image is
inverted, also at the center of curvature, and the
same size as the object because the object and
image are the same distance from the mirror.
Applying the mirror equation to find the image distance, we get:
, matching the ray diagram.
Chapter 23 – Reflection and Mirrors Page 23 - 12
Figure 23.29: A ray diagram for the situation in which
the object is far from the mirror. The squares in the grid
measure 1.0 cm ! 1.0 cm.
Figure 23.30: When the object is at the mirror’s center
of curvature, so is the image.
