Kapoor (mk9499) – oldhomework 34 – Turner – (60230)
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001
(part 1 of 3) 10.0 points
Assume:
The object is on the lefthand side
of the lens indicated in the figure below.
A lens has an index of refraction of 1
.
53.
The lens has a radius of curvature of 17
.
8 cm
on its lefthand side and a radius of curvature
of 8
.
6 cm on its righthand side.
8
.
6 cm
17
.
8 cm
What is the magnitude of the focal length
of the lens?
Correct answer: 31
.
3946 cm.
Explanation:
Basic Concept:
The lens maker’s equa
tion is
1
f
= (
n

1)
parenleftbigg
1
R
1

1
R
2
parenrightbigg
,
where
From the perspective of the object, “
R
” is
positive
if the center of curvature is
behind
a surface, otherwise “
R
” is
negative
.
Given :
n
= 1
.
53
,
R
1
=

17
.
8 cm
,
and
R
2
=

8
.
6 cm
.
Solution:
Applying the lens maker’s equa
tion,
1
f
= (
n

1)
parenleftbigg
1
R
1

1
R
2
parenrightbigg
=
(
n

1) [
R
2

R
1
]
R
1
R
2
f
=
R
1
R
2
(
n

1) [
R
2

R
1
]
=
(

17
.
8 cm)(

8
.
6 cm)
(1
.
53

1) [(

8
.
6 cm)

(

17
.
8 cm)]
= 31
.
3946 cm
,
so
(1)

f

=
31
.
3946 cm
.
002
(part 2 of 3) 10.0 points
The sign of the focal length is
1.
Cannot be determined.
2.
positive.
correct
3.
negative.
Explanation:
See Eq. 1 in the previous part for the sign
of the focal length
f
.
AlternativeExplanation:
Since the lens
is thicker on axis than near its outer edge,
the focal length
f
is positive and the lens is
convergent.
003
(part 3 of 3) 10.0 points
What are the changes to the magnitude and
the sign of the focal length when the lens is
flipped over (or alternatively, the object is on
the righthand side of the lens)?
1.
The magnitude increases and the sign is
unchanged.
2.
The magnitude decreases and the sign is
unchanged.
3.
The magnitude decreases and the sign
changes.
4.
The magnitude increases and the sign
changes.
5.
The magnitude stays the same and the
sign changes.
6.
The magnitude stays the same and the
sign is unchanged.
correct
Explanation:
The position of the object doesn’t matter.
The signs of both
R
1
and
R
2
change and the
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Kapoor (mk9499) – oldhomework 34 – Turner – (60230)
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identity of both
R
1
and
R
2
interchange, if
viewed from the opposite direction.
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 Fall '08
 Turner
 Physics, Work, refractive index, Kapoor

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