Physics 21
Fall 2007
Solution to HW25
Understanding Spherical Mirrors
Consider a concave spherical
mirror with a radius of curvature equal to 60.0 cm. An object 6.00
centimeters tall is placed along the axis of the mirror, 45.0
centimeters from the mirror. You are to find the location and
height of the image. (A) What is the focal length f of this mirror?
30 cm (half the radius of curvature)
(B) Now use the spherical
mirror equation to find the image distance
d
_i.
1/
d
_i = 1/
f
 1/
d
_o = 1/30  1/45 = 1/90, so
f
= 90 cm.
(C) Find the magnification
m
, using
d
_o and
d
_i.
m =

d
_i/
d
_o =
90/45 = 2.00
(D) Finally, use the magnification to find the height of the image.
h
_i = m
h
_o =
2.00 (6.0 cm) = 12.0 cm
(E) Look at the signs of your answers to determine which of the
following describes the image formed by this mirror:
real and
inverted
since m < 0 and image is in front of mirror
(F) Solve the
spherical mirror equation for
d
_i.
1/
d
_i = 1/
f
 1/
d
_o =(
d
_o

f
)/(
f
d
_o) =>
d
_i = (
f
d
_o)/(
d
_o

f
)
(G) What is the magnification
m
? Use your answer from Part F.
m
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 Spring '08
 Hickman
 Physics, ray diagram

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