Solution Derivations for Capa #14
1) An image of the moon is focused onto a screen using a converging lens of focal length
(
f
= 34
.
8
cm
). The diameter of the moon is 3
.
48
×
10
6
m
, and its mean distance from the
earth is 3
.
85
×
10
8
m
. What is the diameter of the moon’s image?
f
= Given
h
= Given (diameter of moon, height of object)
l
= Given (distance to object)
The magnification equation can be used here:
h
h
=

l
l
We are looking for
h
, the height (diameter) of the image on the screen. Since
the moon is so far away, we can treat the light rays as being parallel. Thus, the
image distance
l
is the focal length of the lens.
h
=

hf
l
2) A 0
.
54
cm
high object is placed 8
.
5
cm
in front of a diverging lens whose focal length
is

7
.
5
cm
. What is the height of the image?
h
= Given
l
= Given
f
= Given
We can’t use the magnification equation immediately because we don’t know the
height of the image or the distance to it. But, the lens equation also relates these
quantities. Thus, we can start with it and solve for the first unknown, the image
distance.
1
l
+
1
l
=
1
f
1
l
=
1
f

1
l
l
=
1
1
f

1
l
Now, we can use the magnification equation.
h
h
=

l
l
h
=

hl
l
1
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=

h
l
1
1
f

1
l
=

h
l
1
f

1
l
3) A magnifying glass uses a converging lens with a focal length of 15
.
5
cm
. It produces
a virtual and upright image that is 2.7 times larger than the object. How far is the object
from the lens?
f
= Given
M
= Given
l
= ?
The magnification equation in another form is
M
=

l
l
Thus,
l
=

lM
Now, using the lens equation, the object distance can be solved for
1
f
=
1
l
+
1
l
=
1
l

1
lM
=
M
lM

1
lM
1
f
=
M

1
lM
lM
=
(
M

1)
f
l
=
(
M

1)
f
M
4) What is the image distance? (Think carefully about whether the answer is positive or
negative.)
The image distance formula was a necessary step for the final formula in #3. It
is
l
=

lM
Since
l
was calculated in #3, simple plug this in. Note the signs, the algebra will
take care of it.
5) In the 7 diagrams below, the solid arrow represents the object and the dashed arrow
the image. The rectangle shows the position of an SINGLE OPTICAL ELEMENT. Match
each diagram with the appropriate optical element. (If the first corresponds to B, and the
next 6 to C, enter BCCCCCC.)
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 Fall '08
 ROGERS
 Physics

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