7. Spherical mirror
1) Mirror equation
 



C
h
h
h
h
  1    ;   ;  
d0
di
R
   
   
    2 
di
do
if di    d o  R 2  f
if d o    di  R 2  f
Example:
1 1 2
 
d0 di R
1 1 1
 
d0 di f
R  1.0m
1 2 1
2
1
5.0
 



d i R d 0 1.0m 3.0m 3.0m
d o  3.0m
di 
di  ?
3.0
 0.6m
5.0m
f R 2
f  focus
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2) Magnification
hi
di
m 
ho
do
C
do
di
if
if
m  0 - inverted image
m  0 - erect image
Example: What is magnification in the previous example?
di
0.6m
m

 0.2
do
3.0m
This image is real, inverted,
and 5 times smaller than the object
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3) Graphical method
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4) Image and object at various distances
hi
di
m 
ho
do
f R 2
1
1
1


d0 di
f
f  focus
C
F
C
F
2f=R
f=R/2
0
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magnification image
mirror
do
di
m<0
inverted, real
concave
do>f
di>f
m>1
0<m<1
upright, virtual concave
convex
0<do<f
0<do
di<0
-f<di<0
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Example: You are standing 3.0 m from a convex security mirror in a store.
You estimate the height of your image to be half of your actual height.
Estimate the radius of curvature of the mirror.
d 0  3. 0 m
hi  12 h0
R?
hi
di
m 
ho
do
1
1
1 2

 
d0 di
f
R
d i   12 d 0
1
2
2


d0 do R
R  2d 0  6.0m
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Example: The magnification of a convex mirror is +0.65 for objects 2.2 m
from the mirror. What is the focal length of this mirror?
m  0.65
d 0  2. 2 m
f ?
1
1
1


d0 di
f
hi
di
m 
ho
do
1
1
1


d 0 m d0
f
m d0 0.65  2.2m
f 

m 1
0.65  1
d i  md0
m 1 1

m d0
f
f   4.1m.
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Example: A shaving/makeup mirror is designed to magnify your face
by a factor of 1.33 when your face is placed 20.0 cm in front of it.
(a) What type of mirror is it?
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror.
Solution:
(a) To produce a larger image requires a concave mirror.
(b) The image will be erect and virtual.
(c)
m  1.33
d 0  20.0cm
R?
hi  di
m 
;
ho
do
1
1
1 2

 
d0 di
f
R
di   26.6cm.
f  80.6cm.
R  2 f  280.6cm  161cm.
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Example1: Concave spherical mirrors produce images which
A) are always smaller than the actual object.
B) are always larger than the actual object.
C) are always the same size as the actual object.
D) could be smaller than, larger than, or the same size as the actual object,
depending on the placement of the object.
Example2: Convex spherical mirrors produce images which
A) are always smaller than the actual object.
B) are always larger than the actual object.
C) are always the same size as the actual object.
D) could be larger than, smaller than, or the same size as the actual object,
depending on the placement of the object.
Example3: A single concave spherical mirror produces an image which is
A) always virtual.
B) always real.
C) real only if the object distance is less than f.
D) real only if the object distance is greater than f.
Example4: A single convex spherical mirror produces an image which is
A) always virtual.
B) always real.
C) real only if the object distance is less than f.
D) real only if the object distance is greater than f.
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