PHYSICS 534
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EXERCISE-49
A
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Percy Bridgman was awarded
the Nobel prize for physics in
1946 for his work on high
pressure physics.
Curved Mirrors Part-2 /2
BRIDGMAN
The mirror equation is a geometrical derivation for solving problems with curved mirrors.
where: f = focal length (in metres)
do = Object distance (in metres)
di = Image distance (in metres)
1
1
1


f do di
and
M
hi
d i

ho
do
where: M = magnification factor (no units)
hi = height of image (in metres)
ho = height of object (in metres)
Be sure to observe the following sign conventions when using this formula:
 All distances are measured from the vertex of a curved mirror.
 Distances of objects and real images are positive.
 Distances of virtual images are negative.
 Object and image heights are positive when upright and negative when inverted.
Parabolic mirrors are used as reflectors for searchlights, flashlights, projectors and automobile headlights.
1.
An object is 60 cm from a converging mirror whose radius of curvature is 30 cm.
Determine the characteristics of the image.
d  60 cm
f  15 cm
1 1
1
 

f do di
1 1 1
1
1
 


 d i  20 cm
d i f d o 15 cm 60 cm
M
2.
 d i  (20 cm )

  0.33
do
60 cm
Real
Type: ________________
(real or virtual)
20
cm
in front of mirror
Location: ________________
(Reducedimage)
Magnification: -0.33
________________
Attitude:
Inverted
______________
(upright or inverted)
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.
An object is 25 cm from a concave mirror whose focal length is 15 cm. Determine the
characteristics of the image.
d  25 cm

f  15 cm
1 1
1


f do di
1 1 1
1
1
 


 d i  37.5 cm
d i f d o 15 cm 25 cm
 d i  (37.5 cm )
M

  1.5
do
25 cm
PHYSICS 534  OPTICS  AnsPhysics Ex-49.DOC
Real
Type: ________________
(real or virtual)
.5cminfront of mirror
Location: 37
________________
Magnification: -1
________________
.5(Magnifiedimage)
Attitude:
Inverted
______________
(upright or inverted)
© 1999 S. Lancione
Page 1 /4
3.
An object is placed 7.5 cm from a concave mirror that has a focal length of 15 cm.
Determine the characteristics of the image.
d o  7.5 cm f  15 cm
1 1
1
 

f do di
1 1 1
1
1
 


 d i   15 cm
d i f d o 15 cm 7.5 cm
M
4.
 d i  (15 cm )

2
do
7.5 cm
Virtual
Type: ________________
(real or virtual)
15
cm behind mirror
Location: ________________
2 (Magnified image)
Magnification: ________________
Attitude:
Upright
______________
(upright or inverted)
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.
A converging mirror has a focal length of 15 cm. Where would you place an object
in front of this mirror in order to produce an upright, virtual image, twice as tall as
the object? [7.5 cm]
____________________________________________________________________
f  15 cm
1 1
1
1
1
1
1
1
do  ?
____________________________________________________________________








f do di do  2do do 2do 2do
hi  2ho
____________________________________________________________________
1
1
M2
 Since

____________________________________________________________________
f 2do
 di
 M
____________________________________________________________________
f 15 cm
do
 do  
 7.5 cm
2
2
____________________________________________________________________
 di  di
or d o 

M
2
____________________________________________________________________
 di   2 do
____________________________________________________________________
5.
What is the focal length of a concave mirror when an object that is placed 2 cm in
front of the mirror produces an image that is seen 5 cm behind the mirror? [3.3 cm]
1 1
1
____________________________________________________________________


f
d
d
o
i
____________________________________________________________________
f ?
1
1
d o  2 cm


____________________________________________________________________
2 cm  5 cm
d i   5 cm
52
____________________________________________________________________

10 cm
3

____________________________________________________________________
10 cm
10 cm
Thus : f 
 3.3 cm
____________________________________________________________________
3
____________________________________________________________________
____________________________________________________________________
PHYSICS 534  OPTICS  AnsPhysics Ex-49.DOC  Curved Mirrors Part-2 /2
Page 2 /4
6.
A concave mirror has a focal length of 30 cm. A square object, 4 cm per edge, is
situated with its center 10 cm in front of the mirror. Determine:
a) The position (center) of the image.
[-15 cm]
_________________________________________________________________
1 1
1


_________________________________________________________________
f do di
f  30 cm
d o  10 cm
_________________________________________________________________
1 1 1
or
 
d

?
i
_________________________________________________________________
d
f d
i
o
1
1
_________________________________________________________________

30 cm 10 cm
_________________________________________________________________
Thus : d i   15 cm
_________________________________________________________________
b) The area of the image.
[36 cm2]
_________________________________________________________________
h
d
Since :
i

i
hi  ?
_________________________________________________________________
ho
do
 diho
h o  4 cm
_________________________________________________________________
Thus : h i 
do
d o  10 cm
_________________________________________________________________
 (15 cm )(4 cm )
d i   15 cm

_________________________________________________________________
10 cm
 6 cm
_________________________________________________________________
Answer : 6 cm  6 cm  36 cm
_________________________________________________________________
2
7.
Illustrated below is an object situated in front of a convex mirror. Graphically, find the
image and state its characteristics.
Reflected
rays
Object
Image
F
C
Extended rays
____________________________________________________________________
The image is virtual, upright, reduced and located behind the mirror.
____________________________________________________________________
____________________________________________________________________
PHYSICS 534  OPTICS  AnsPhysics Ex-49.DOC  Curved Mirrors Part-2 /2
Page 3 /4
8.
An object is placed 10 cm in front of a convex mirror whose focal length is 15 cm.
Determine the characteristics of the image.
____________________________________________________________________
1 1
1
____________________________________________________________________
f  15 cm
 di


M
f
d
d
o
i
d o  10 cm
____________________________________________________________________
do
1
1
1
di  ?
 (30 cm )
Thus :
 
____________________________________________________________________

d
f
d
i
o
M ?
10 cm
____________________________________________________________________
1
1
3


15 cm 10 cm
____________________________________________________________________
d i   30 cm
____________________________________________________________________
The image is virtual (since di is negative), upright (since M is positive),
____________________________________________________________________
three times larger than the object (since M = 3) and located behind mirror.
____________________________________________________________________
9.
When an object is 30 cm in front of a concave mirror, its image is real and situated
15 cm from the mirror. Determine the location of the image if the object is placed
6.0 cm from the mirror. [15 cm]
d o  6.0 cm
____________________________________________________________________
d  30 cm
di  ?
o
d i  15 cm
____________________________________________________________________
f  10 cm
f  ?
1 1
1
____________________________________________________________________
Since : 

Since :
1

1

1
f
d
d
o
i
f do di
____________________________________________________________________
1 1 1
1
1
30 cm 15 cm
di f do
____________________________________________________________________
Thus : f  10 cm
1
1


10 cm 6 cm
____________________________________________________________________
d i   15 cm
____________________________________________________________________
 


10. Fill in the four (4) missing quantities:
MIRROR
TYPE
FOCAL
LENGTH
Concave
Convex
4 cm

23.3 cm
OBJECT
IMAGE
DISTANCE DISTANCE

3 cm
10 cm
-12 cm
-7 cm
OBJECT
HEIGHT
2 cm
1 cm
IMAGE
HEIGHT
8 cm
 0.7 cm


PHYSICS 534  OPTICS  AnsPhysics Ex-49.DOC  Curved Mirrors Part-2 /2
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