3414
Chapter 34
E
XECUTE
:
The image is behind the lens, so
0
s
′ <
. The thinlens equation gives
1
1
1
1
1
1
4.17 cm
5.00 cm
25.0 cm
s
s
s
f
s
+
=
⇒
=
−
⇒
=
′
−
, on the same side of the lens as the ant.
E
VALUATE
:
Since
0
s
′ <
, the image will be erect.
34.52.
I
DENTIFY
:
Apply Eq.(34.24).
S
ET
U
P
:
1
160 mm
5.0 mm
165 mm
s
′ =
+
=
E
XECUTE
:
(a)
1
1
2
(250 mm)
(250 mm)(165 mm)
317.
(5.00 mm)(26.0 mm)
s
M
f f
′
=
=
=
(b)
The minimum separation is
4
0.10 mm
0.10 mm
3.15
10
mm.
317
M
−
=
=
×
E
VALUATE
:
The angular size of the image viewed by the eye when looking through the microscope is 317 times
larger than if the object is viewed at the nearpoint of the unaided eye.
34.53.
(a) I
DENTIFY
and
S
ET
U
P
:
Figure 34.53
Final image is at
∞
so the object for the eyepiece is at its focal point. But the object for the eyepiece is the image
of the objective so the image formed by the objective is 19.7 cm ° 1.80 cm = 17.9 cm to the right of the lens.
Apply Eq.(34.16) to the image formation by the objective, solve for the object distance
s
.
0.800 cm;
17.9 cm;
?
f
s
s
′
=
=
=
1
1
1
1
1
1
, so
s
f
s
s
f
s
f
s
s f
′ −
+
=
=
−
=
′
′
′
E
XECUTE
:
(17.9 cm)(
0.800 cm)
8.37 mm
17.9 cm
0.800 cm
s f
s
s
f
′
+
=
=
= +
′ −
−
(b) S
ET
U
P
:
Use Eq.(34.17).
E
XECUTE
:
1
17.9 cm
21.4
0.837 cm
s
m
s
′
= −
= −
= −
The linear magnification of the objective is 21.4.
(c) S
ET
U
P
:
Use Eq.(34.23):
1
2
M
m M
=
E
XECUTE
:
2
2
25 cm
25 cm
13.9
1.80 cm
M
f
=
=
=
1
2
( 21.4)(13.9)
297
M
m M
=
= −
= −
E
VALUATE
:
M
is not accurately given by
1
1
2
(25 cm)
/
311,
s
f f
′
=
because the object is not quite at the focal point
of the objective
1
1
(
0.837 cm and
0.800 cm).
s
f
=
=
34.54.
I
DENTIFY
:
Eq.(34.24) can be written
1
1
2
2
1
s
M
m M
M
f
′
=
=
.
S
ET
U
P
:
1
1
120 mm
s
f
′ =
+
E
XECUTE
:
16 mm :
120 mm
16 mm
136 mm;
16 mm
f
s
s
′
=
=
+
=
=
.
1
136 mm
8.5
16 mm
s
m
s
′
=
=
=
.
1
124 mm
4 mm :
120 mm
4 mm
124 mm;
4 mm
31
4 mm
s
f
s
s
m
s
′
′
=
=
+
=
=
⇒
=
=
=
.
1
122 mm
1.9 mm :
120 mm
1.9 mm
122 mm;
1.9 mm
64
1.9 mm
s
f
s
s
m
s
′
′
=
=
+
=
=
⇒
=
=
=
.
The eyepiece magnifies by either 5 or 10, so:
(a)
The maximum magnification occurs for the 1.9mm objective and 10x eyepiece:
1
e
(64)(10)
640.
M
m M
=
=
=
(b)
The minimum magnification occurs for the 16mm objective and 5x eyepiece:
1
e
(8.5)(5)
43.
M
m M
=
=
=
E
VALUATE
:
The smaller the focal length of the objective, the greater the overall magnification.
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Geometric Optics
3415
34.55.
I
DENTIFY
:
number
/
f
f
D
=
S
ET
U
P
:
1.02 m
D
=
E
XECUTE
:
19.0
(19.0)
(19.0)(1.02 m)
19.4 m.
f
f
D
D
=
⇒
=
=
=
E
VALUATE
:
Camera lenses can also have an
f
number of 19.0. For a camera lens, both the focal length and lens
diameter are much smaller, but the
f
number is a measure of their ratio.
34.56.
I
DENTIFY
:
For a telescope,
1
2
f
M
f
= −
.
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 Spring '06
 Buchler
 Physics

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