Chapter 34: Mirrors
We will consider three varieties of mirrors
Plane
Mirror
Spherical
Convex
Mirror
Spherical
Concave
Mirror
Photos from Fishbane, et al.
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Chapter The
34:Spherical
MirrorsConcave Mirror
Reflected rays
focus at one point.
Photo from Fishbane, et al.
Four Incident Rays
Four Reflected Rays
2
Find the center
of this spherical
mirror.
The white lines
are all normal to
the surface of
the mirror.
Center of curvature
Photo from Fishbane, et al.
Chapter The
34:Spherical
MirrorsConcave Mirror
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Chapter The
34:Spherical
MirrorsConcave Mirror
Focal Point: The
place where the
reflections of
parallel rays
converge.
Center of curvature
focal length, f
“optic
axis”
focal length, f
r
f 
2
radius of curvature, r
True for concave & convex mirrors.
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Chapter 34: Mirrors
Optical Ray Diagram: a line drawing depicting a
small number of key light rays. For a mirror, an
optical ray diagram should include:
1. Parallel Ray. A ray parallel to the optic axis
which passes through an object.
2. Focal Ray. A ray that passes through both the
focal point and an object.
3. Chief Ray. A ray that passes through both the
center of curvature and an object.
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Chapter The
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MirrorsConcave Mirror
1. Parallel ray. All rays parallel to the optic axis pass
through the focal point.
object
f
“optic
axis”
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Chapter The
34:Spherical
MirrorsConcave Mirror
2. Focal ray. A ray that passes through the focal
point is also parallel to the optic axis after reflection.
object
f
“optic
axis”
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Chapter The
34:Spherical
MirrorsConcave Mirror
3. Chief ray. A ray that passes through the center of
curvature hits the mirror normal to its surface and
reflects directly back
object
f
“optic
axis”
center of
curvature
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Chapter The
34:Spherical
MirrorsConcave Mirror
Image. The result of converging reflected rays.
Draw all three key rays. The
reflections converge at the image.
object
f
inverted image: an
image which is seen
below the optic axis.
image
(notice it’s small)
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Chapter The
34:Spherical
MirrorsConcave Mirror
Example 1: Locate the image in this mirror.
f
In this example the reflected rays don’t converge.
Does that mean there is no image?
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Chapter The
34:Spherical
MirrorsConcave Mirror
In this case, the image is behind the mirror.
Extend the reflected rays behind the mirror. They
converge on the image.
f
Notice the image is (1) above the optic axis, (2) behind
the mirror, and (3) larger than the object.
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Chapter 34: Mirrors
Virtual Image:
Behind the mirror. Light doesn’t pass through it.
Real Image:
In front of the mirror. Light passes through it.
Inverted Image:
Below the optic axis. Upside down. m<0
Upright Image:
Above the optic axis. Right-side-up. m>0
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Chapter 34: Mirrors
Where is the image?
hi
ho
f
so
si
f
The mirror equation:
1 1 1
 
so si f
Caution: distances
behind the mirror are
negative.
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Chapter The
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MirrorsConvex Mirror
The Convex Mirror
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Chapter The
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MirrorsConvex Mirror
The Convex Mirror
Focal Point
=r/2
Extrapolate the reflected rays back to find the focal point.
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Chapter The
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MirrorsConvex Mirror
The Convex Mirror
parallel ray
r
focal ray

f=r/2
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Chapter The
34:Spherical
MirrorsConvex Mirror
Example 2: You are standing so=3.0 m in front of a
convex mirror. The height of your image is half your
actual height and is upright (m=+0.5). What is the
radius of curvature, r, of the mirror?
so=3.0 m
si
r=2f

f=r/2
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Chapter The
34:Spherical
MirrorsConvex Mirror
Example 2: You are standing so=3.0 m in front of a
convex mirror. The height of your image is half your
actual height and is upright (m=+0.5). What is the
radius of curvature, r, of the mirror?
radius of curvature: r=2f
How can we find f?
First, we need di:
1 1 1
 
so si f
si
m
 0.5
so
si  0.5so
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Chapter The
34:Spherical
MirrorsConvex Mirror
Example 2: You are standing so=3.0 m in front of a
convex mirror. The height of your image is half your
actual height and is upright (m=+0.5). What is the
radius of curvature, r, of the mirror?
1
1
1


so (0.5so ) f
1
1
1


3.0 m 1.5 m f
f  3 m
r=2f=-6m

f=r/2
A negative radius of curvature indicates convex.
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