CHAPTER 18
1. Sally’s face is 75 cm in front of a plane
mirror. Where is the image of Sally’s
face?
75 cm behind the mirror
2. A concave mirror has a focal length of
10.0 cm. What is its radius of curvature?
r 5 2f 5 2(10.0 cm) 5 20.0 cm
3. Light from a distant star is collected by a
concave mirror that has a radius of
curvature of 150 cm. How far from the
mirror is the image of the star?
r
150 cm
f 5 }} 5 }} 5 75.0 cm
2
2
1
1
1
}} 5 }} 1 }}
f
di
do
but do is extremely large, so
1
1
}} 5 }} or di 5 f 5 75.0 cm
f
di
4. An object is placed 25.0 cm away from a
concave mirror that has a focal length of
5.00 cm. Where is the image located?
1
1
1
}} 5 }} 1 }} , so
f
d1
do
do f
(25.0 cm)(5.00 cm)
di 5 }} 5 }}}
do 2 f
25.0 cm 2 5.00 cm
5 6.25 cm
or 6.25 cm in front of the mirror
For a concave mirror, an object and
its image have the same height when
the object is two focal lengths from
the mirror. Therefore,
48.4 cm
48.4 cm 5 2f, or f 5 }}
2
5 24.2 cm
6. An object placed 50.0 cm from a concave
mirror gives a real image 33.3 cm from
the mirror. If the image is 28.4 cm high,
what is the height of the object?
hi
–di
–33.3 cm
m 5 }} 5 }} 5 }} 5 –0.666
ho
do
50.0 cm
92
Supplemental Problems Manual
7. An object, 15.8 cm high, is located
87.6 cm from a concave mirror that has a
focal length of 17.0 cm.
a. Where is the image located?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(87.6 cm)(17.0 cm)
di 5 }} 5 }}}
do 2 f
87.6 cm 2 17.0 cm
5 21.1 cm
b. How high is the image?
hi
–di
–21.2 cm
m 5 }} 5 }} 5 }} 5 0.242, so
ho
do
87.6 cm
hi 5 mho 5 (–0.242)(15.8 cm)
5 –3.82 cm; inverted
The negative sign indicates an
inverted image.
8. The image of the moon is formed by a
concave mirror whose radius of curvature
is 4.20 m at a time when the moon’s
distance is 3.80 3 105 km. What is the
diameter of the image of the moon if the
diameter of the moon is 3480 km?
r
4.20 m
f 5 }} 5 }} 5 2.10 m
2
2
1
1
1
}} 5 }} 1 }} , but do is extremely
f
di
do
large, so
1
1
}} 5 }} , or di 5 f 5 2.10 m
f
di
5 2.10 3 10–3 km
hi
–di
–(2.10 3 10–3 km)
m 5 }} 5 }} 5 }}}
ho
do
3.80 3 105 km
5 –5.53 3 10–9
hi 5 mho 5 (–5.53 3 10–9)(3480 km)
5 –1.92 3 10–5 km
5 –1.92 cm; inverted
The negative sign indicates an
inverted image.
Physics: Principles and Problems
Copyright © by Glencoe/McGraw-Hill
5. An object and its image as seen in a
concave mirror are the same height when
the object is 48.4 cm from the mirror.
What is the focal length of the mirror?
hi
–28.4 cm
So ho 5 }} 5 }} 5 42.6 cm
m
–0.666
m is the negative, so the image is
inverted and hi is negative.
Chapter 18 (continued)
9. A shaving mirror has a radius of curvature
of 30.0 cm. When a face is 10.0 cm away
from the mirror, what is the
magnification of the mirror?
A shaving mirror is concave.
r
30.0 cm
f 5 }} 5 }} 5 15.0 cm
2
2
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(10.0 cm)(15.0 cm)
di 5 }} 5 }}}
do 2 f
10.0 cm 2 15.0 cm
5 –30 cm
hi
–di
–(–30 cm)
m 5 }} 5 }} 5 }} 5 3.0
ho
do
10.0 cm
m is positive, so the image is erect.
10. A convex mirror has a focal length of
–16 cm. How far behind the mirror does
the image of a person 3.0 m away
appear?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(3.0 m)(–0.16 m)
di 5 }} 5 }}}
do 2 f
3.0 m 2 (–0.16 m)
5 –0.15 m
Copyright © by Glencoe/McGraw-Hill
or 15 cm behind the mirror.
11. How far behind the surface of a convex
mirror, focal length of –6.0 cm, does a car
10.0 m from the mirror appear?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(10.0 m)(–0.060 m)
di 5 }} 5 }}}
do 2 f
10.0 m 2 (–0.060 m)
5 –0.060 m
or 6.0 cm behind the mirror.
12. A converging lens has a focal length of
25.5 cm. If it is placed 72.5 cm from an
object, at what distance from the lens will
the image be?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(72.5 cm)(25.5 cm)
di 5 }} 5 }}}
do 2 f
72.5 cm 2 25.5 cm
5 39.3 cm
Physics: Principles and Problems
13. If an object is 10.0 cm from a converging
lens that has a focal length of 5.00 cm,
how far from the lens will the image be?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(10.0 cm)(5.00 cm)
di 5 }} 5 }}}
do 2 f
10.0 cm 2 5.00 cm
5 10 cm
14. The focal length of a lens in a box camera
is 10.0 cm. The fixed distance between
the lens and the film is 11.0 cm. If an
object is clearly focused on the film, how
far must the object be from the lens?
1
1
1
}} 5 }} 1 }} , so
f
di
do
dof
(11.0 cm)(10.0 cm)
di 5 }} 5 }}}
do 2 f
11.0 cm 2 10.0 cm
5 1.1 3 102 cm
15. An object 3.0 cm tall is placed 22 cm in
front of a converging lens. A real image
is formed 11 cm from the lens. What is
the size of the image?
hi
–di
–(11 cm)
m 5 }} 5 }} 5 }} 5 –0.50, so
ho
do
22 cm
hi 5 mho 5 (–0.50)(3.0 cm)
5 –1.5 cm; inverted
The negative sign indicates an
inverted image.
16. An object 3.0 cm tall is placed 20 cm in
front of a converging lens. A real image
is formed 10 cm from the lens. What is
the focal length of the lens?
1
1
1
1
1
}} 5 }} 1 }} 5 }} 1 }}
f
di
do
10 cm
20 cm
3
5 }}
20 cm
20 cm
so f 5 }} 5 6.7 cm
3
17. What is the focal length of the lens in
your eye when you read a book that is
35.0 cm from your eye? The distance
from the lens to the retina is 0.19 mm.
1
1
1
}} 5 }} 1 }} , so
f
di
do
dido
(0.19 mm)(350 mm)
f 5 }} 5 }}}
di 1 do
0.19 mm 1 350 mm
5 0.19 mm
Supplemental Problems Manual 93
Chapter 18 (continued)
18. When an object 5.0 cm tall is placed
12 cm from a converging lens, an image
is formed on the same side of the lens as
the object but the image is 61 cm away
from the lens. What is the focal length of
the lens?
dido
(–61 cm)(12 cm)
f 5 }} 5 }}
di 1 do
–61 cm 1 12 cm
5 14.9 cm
19. When an object 5.0 cm tall is placed
12 cm from a converging lens, an image
is formed on the same side of the lens as
the object but the image is 61 cm away
from the lens. What is the size of the
image?
hi
–di
}} 5 }}
ho
do
–di
–61
hi 5 ho }} 5 5.0 cm – }}
do
12
1 2
1
2
5 25.4 cm; image is erect.
Copyright © by Glencoe/McGraw-Hill
94
Supplemental Problems Manual
Physics: Principles and Problems