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Chapter 34: Mirrors
1
We will consider three varieties of mirrors
Spherical ConcaveMirror
PlaneMirror
Spherical ConvexMirror
Photos from Fishbane, et al.
Chapter 34: Mirrors
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Four Incident Rays
Four Reflected Rays
Pho
to f
rom
Fis
hban
e, e
t al
.
The Spherical Concave Mirror
Reflected rays focus at one point.
Chapter 34: Mirrors
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Find the center of this spherical mirror.
The white lines are all normal to the surface of the mirror.
The Spherical Concave Mirror
Pho
to f
rom
Fis
hban
e, e
t al
.Center of curvature
Chapter 34: Mirrors
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radius of curvature, r
Focal Point: The place where the reflections of parallel rays converge.
focal length, f
2
rf
focal length, f
“optic axis”
The Spherical Concave Mirror
True for concave & convex mirrors.
Center of curvature
Chapter 34: Mirrors
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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.
Chapter 34: Mirrors
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“optic axis”
object
1. Parallel ray. All rays parallel to the optic axis pass through the focal point.
f
The Spherical Concave Mirror
Chapter 34: Mirrors
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“optic axis”
object
2. Focal ray. A ray that passes through the focal point is also parallel to the optic axis after reflection.
f
The Spherical Concave Mirror
Chapter 34: Mirrors
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“optic axis”
object
f
3. Chief ray. A ray that passes through the center of curvature hits the mirror normal to its surface and reflects directly back
center of curvature
The Spherical Concave Mirror
Chapter 34: Mirrors
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object
f
The Spherical Concave Mirror
Image. The result of converging reflected rays.
Draw all three key rays. The reflections converge at the image.
image(notice it’s small)
inverted image: an image which is seen below the optic axis.
Chapter 34: Mirrors
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The Spherical Concave Mirror
f
Example 1: Locate the image in this mirror.
In this example the reflected rays don’t converge. Does that mean there is no image?
reflected rays
Chapter 34: Mirrors
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The Spherical Concave 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.
Chapter 34: Mirrors
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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
Chapter 34: Mirrors
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fhiho
Where is the image?
f
so si
The mirror equation:fss io
111
Caution: distances behind the mirror are negative.
Chapter 34: Mirrors
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The Convex Mirror
The Spherical Convex Mirror
Chapter 34: Mirrors
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The Convex Mirror
Focal Point=r/2
Extrapolate the reflected rays back to find the focal point.
The Spherical Convex Mirror
Chapter 34: Mirrors
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The Convex Mirror
f=r/2
r
chief rayparallel ray
The Spherical Convex Mirror
focal ray
Chapter 34: Mirrors
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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?
r=2f
f=r/2
so=3.0 m
The Spherical Convex Mirror
si
Chapter 34: Mirrors
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radius of curvature: r=2f
How can we find f?
First, we need di: 5.0 o
i
s
sm oi ss 5.0
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?
The Spherical Convex Mirror
fss io
111
Chapter 34: Mirrors
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m 3
1
m 5.1
1
m 0.3
1
1
)5.0(
11
f
f
fss oo
r=2f=-6m
f=r/2
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?
The Spherical Convex Mirror
A negative radius of curvature indicates convex.
