344
Chapter 34
34.12.
IDENTIFY:
sf
s
s
f
′ =
−
and
f
m
f
s
=
−
.
SET UP:
With
f
f
=−
,
s f
s
s
f
′=−
+
and
f
m
s
f
=
+
.
EXECUTE:
The graphs are given in Figure 34.12.
(a)
0for
0.
sf
s
′
>−
<
<
(b)
0 for s
and
0.
s
′
<<
−
<
(c)
If the object is at infinity, the image is at the outward going focal point.
(d)
If the object is next to the mirror, then the image is also at the mirror
(e)
The image is erect (magnification greater than zero) for
.
s
f
(f)
The image is inverted (magnification less than zero) for
.
s
f
< −
(g)
The image is larger than the object (magnification greater than one) for
20
.
fs
−
(h)
The image is smaller than the object (magnification less than one) for
0and
2
.
s
><
−
EVALUATE:
For a real image
(0
)
s
>
, the image formed by a convex mirror is always virtual and smaller than the
object.
Figure 34.12
34.13.
IDENTIFY:
11 1
s
+=
′
and
ys
m
′′
==
−
.
SET UP:
2.00
m
=+
and
1.25 cm
s
=
. An erect image must be virtual.
EXECUTE: (a)
sf
s
s
f
′ =
−
and
f
m
s
f
−
. For a concave mirror,
m
can be larger than 1.00. For a convex mirror,
f
f
so
f
m
s
f
+
and
m
is always less than 1.00. The mirror must be concave (
0)
f
>
.
(b)
1
s
s
f
ss
′ +
=
′
.
ss
f
s
s
′
=
′
+
.
2.00
s
m
s
′
and
2.00
s
s
′ = −
.
(2
.
0
0)
2.00
2.50 cm
2.00
ss
−
+
=
+
−
.
25
.
0
0
c
m
Rf
+
.
(c)
The principal ray diagram is drawn in Figure 34.13.
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345
EVALUATE:
The principalray diagram agrees with the description from the equations.
Figure 34.13
34.14.
IDENTIFY:
Apply
11 1
s
sf
+=
′
and
s
m
s
′
= −
.
SET UP:
For a concave mirror,
0
R
>
.
32.0 cm
R
=
and
16.0 cm
2
R
f
==
.
EXECUTE:
(a)
s
′
.
(12.0 cm)(16.0 cm)
48.0 cm
12.0 cm 16.0 cm
sf
s
′
=
−
−−
.
48.0 cm
4.00
12.0 cm
s
m
s
′
−
=−
=+
.
(b)
48.0 cm
s
′=−
, so the image is 48.0 cm to the right of the mirror.
0
s
′ <
so the image is virtual.
(c)
The principalray diagram is sketched in Figure 34.14. The rules for principal rays apply only to paraxial rays.
Principal ray 2, that travels to the mirror along a line that passes through the focus, makes a large angle with the
optic axis and is not described well by the paraxial approximation.
Therefore, principal ray 2 is not included in the
sketch.
EVALUATE:
A concave mirror forms a virtual image whenever
s
f
<
.
Figure 34.14
34.15.
IDENTIFY:
Apply Eq.(34.11), with
.
R
s
′
→∞
is the apparent depth.
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 Spring '06
 Buchler
 Physics

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