Howard (clh2528) – Homework #2 – shubeita – (57885)
1
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001(part1of2)10.0points
An object located 32
.
5 cm in front of a lens
forms an image on a screen 10
.
5 cm behind
the lens.
Find the focal length of the lens.
Correct answer: 7
.
93605 cm.
Explanation:
BasicConcepts:
1
p
+
1
q
=
1
f
m
=
h
′
h
=

q
p
ConvergingLens
f >
0
∞
>p>f
f <q<
∞
0
>m>
∞
f >p>
0
∞
<q<
0
∞
>m>
1
DivergingLens
f <
0
∞
>p>
0
f <q<
0
0
<m<
1
Solution:
The formula relating the focal
length to the image distance
s
′
and the object
distance
s
is
1
s
+
1
s
′
=
1
f
so
f
=
ss
′
s
+
s
′
=
(32
.
5 cm) (10
.
5 cm)
(32
.
5 cm) + (10
.
5 cm)
= 7
.
93605 cm
.
002(part2of2)10.0points
What is the magnification of the object?
Correct answer:

0
.
323077.
Explanation:
Magnification is
M
=

s
′
s
=

(10
.
5 cm)
(32
.
5 cm)
=

0
.
323077
.
003
10.0points
S
E
F
W
P
Q
Which
of the glass lenses
above,
when
placed in air, will cause rays of light (par
allel to the central axis) to
converge
?
1.
F, S, and E
2.
F, Q, and P
3.
S and E
4.
S and Q
5.
F, W, and E
6.
F, W, and Q
correct
7.
F, S, W, and P
8.
F, E, and P
9.
W and Q
10.
F, S, Q, and P
Explanation:
convergent
divergent
Use the
lensmakers’equation
1
f
= (
n

1)
parenleftbigg
1
R
1

1
R
2
parenrightbigg
,
where
R
1
and
R
2
are + (or

) if the center of
curvature is behind (or in front of) the lens.
To cause parallel rays of light to converge,
f
must be positive (
n>
1).
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Howard (clh2528) – Homework #2 – shubeita – (57885)
2
F:
R
1
>
0 and
R
2
=
∞
, =
⇒
f >
0
,
therefore
convergent.
S:
R
1
=
∞
and
R
2
>
0, =
⇒
f <
0
,
therefore
divergent.
W:
R
1
>
0 and
R
2
>
0, but

R
1

>

R
2

,
=
⇒
f >
0
,
therefore convergent.
E:
R
1
<
0 and
R
2
<
0, but

R
1

<

R
2

,
=
⇒
f <
0
,
therefore divergent.
Q:
R
1
<
0 and
R
2
<
0, but

R
1

>

R
2

,
=
⇒
f >
0
,
therefore convergent.
P:
R
1
>
0 and
R
2
>
0, but

R
1

=

R
2

,
=
⇒
f
=
∞
,
therefore neither convergent
or divergent.
Thus, lenses F, W, and Q are convergent
lenses and Lenses S and E are divergent.
Alternate(Elegant)Solution:
ConvergingLens:
The glass is thicker on
the axis than at the edge.
F, W, and Q satisfy these conditions for a
converging lens (
f >
0).
Diverging Lens:
The glass is thinner on
the axis than at the edge.
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 Spring '08
 RITCHIE/LANG
 Work, Thin lens

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