Day 6
The Mirror Equation
____________________
The Magnification Equation
___________________
*** Don’t forget the relationship between the focal length and the radius of curvature: _____________
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Rules for using the equations
a) All distances are measured from the vertex, while all heights are measured from the principal axis.
b) Upright images have ________ heights and Inverted images have ________ heights.
c) Real images/objects have _________ distances ….
…. and Virtual images/objects have ________ distances.
d) Focal lengths for converging mirrors are ________ …..
…. Focal lengths for diverging mirrors are __________.
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In-Class Examples:
A) A 50 cm tall object stands 1 meter away from a converging mirror whose radius of curvature is
1.2 meters. Find the …
i)
image distance.
ii) image height.
iii) magnification of the mirror.
B) A woman is putting make-up on using a concave mirror. Her face is twice as large as usual in
the mirror when she is 10 cm away from it. Find the…
i)
image distance.
ii) mirror’s focal length.
iii) image characteristics.
C) A 4 meter tall man is standing in front of a large, converging mirror of focal length 3 meters. His
image in mirror is upside down, as well as 3 times smaller than he is. Find his distance from the
mirror as well as the image distance.
TOUGH PROBLEM
The last problem uses the “ _________________ Method”
D) An object is placed in front of a converging mirror, and an image is created that is 4 times as
large as it. If the radius of curvature of the mirror is 15 cm, find the …
i) object distance.
ii) image distance. iii) possible magnification(s) of the mirror.
HOMEWORK PROBLEMS
It is HIGHLY recommended that you begin every problem by drawing a ray diagram so that you
know what answers to expect before using the equations.
1) An object that is 5 cm tall is placed 10 cm away from a converging mirror whose focal length is
3 cm. Find the …
a) image distance.
b) image height.
c) image characteristics.
2) An object is placed 6 cm away from a converging mirror whose focal length is 4 cm. The image
formed in the mirror is 3 cm tall. Find the …
a) image distance.
b) image characteristics.
c) object height
3) A bird, 16 in tall, is standing in front of a converging mirror whose radius of curvature is 20 in.
The bird sees its image in the mirror, but it is upside down. If the birds image distance is 14 in,
find the …
a) object distance
c) image height
c) image characteristics
4) A man is shaving at a distance of 30 cm from his concave shaving mirror. He sees an image of
himself that is located 50 cm behind the mirror. Find…
a) the mirror’s focal length.
b) the magnification of the mirror.
5) A 4cm tall object is placed 40 cm in front of a concave, converging mirror whose focal length is
10 cm. Find the …
a) image distance.
b) image height.
c) image characteristics.
6) A 6m tall object is placed 4 m in front of a concave, converging mirror whose focal length is 3m.
Find the …
a) image distance. b) magnification of the mirror.
c) image characteristics.
7) Determine the image distance for a converging mirror that has a focal length of 15 cm if the
object is placed
a. 40 cm from the mirror. What TYPE of image is this?
b. 10 cm from the mirror. What TYPE of image is this?
8) A 3in tall birthday candle is placed in front of concave, converging mirror whose focal length is
10 in. The image in the mirror is upright, and is 6 in tall. Find the image distance, and then state
the orientation/attitude and type of the image.
9) A woman looks at herself in a magnifying converging cosmetic mirror whose focal length is 20
cm. If her face is 6 cm from the mirror,
a. at what distance from the mirror is her image?
b. what is the magnification of her face?
10) A copy machine has a converging lens with a focal length of 40 cm. How far from the lens must
documents be placed if the copies are to be exactly the same size as the original?
11) A 10 meter tall flagpole that is 25 m away is seen in a concave, converging mirror of focal length
20 cm. Find the image distance and the image height, and then list the 4 characteristics
(attitude, size, type, location) of the image. (Hint: watch your units)
12) A concave, converging mirror has a focal length of 20 cm. Find the locations that you would
place an object in order to get…
i.
A real image. ______
ii.
A virtual image ______
a)
do < 20 cm
b) do = 20 cm
c)
do > 20 cm
iii.
No image. ______
iv.
An image whose magnification is greater than +1. ____
e)
do > 40 cm
v.
An image where 0 < M < 1. ______
f)
40 > do > 0 cm
vi.
An image where M < 0. ______
vii.
An image whose magnification is -1. ______
viii.
ix.
d) 40 > do > 20 cm
g) No location
h)
do = 40 cm
i)
40 > do > 0 cm BUT do ≠ 20 cm
An image where |M| > 1. ______
An image where -1 < M < 0. ______
Only 1 answer is correct per line. You can
use an answer more than once if necessary.
(Substitution Method)
13) An object stands in front of a converging mirror of radius 40 cm, creating an image that is 5
times smaller than the image itself. Where is the object located (in both numbers and with
words)?
14) Where must an object be placed in front of a concave mirror of focal length 15 cm so that it
creates an image that is 4 times larger. (Hint: be careful )
15) An object placed 4 meters in front of a large converging mirror creates a real image that is 5
times larger than the object itself. Find the focal length of the mirror.
SOLUTIONS
Fill in the blank solutions for the notes:
1 1 1
 
f do d i

hi
d
 i
ho
do
f=½R
+, -, +, -, +, -,
“Substitution”
In-Class Examples

A)
di = 1.5 m
hi = -75 cm
M = -1.5
B)
di = -20 cm
f = 20 cm
C)
do = 12 m
D)
do = 5.625 cm, di = -22.5 cm ,
Virtual, Larger, Upright, Behind the mirror, Perverted
di = 4 m
M = 4x
OR
do = 9.375 cm, di = 37.5 cm, M = -4x
Homework Problems
1) 4.286 cm, -2.143 cm, Inverted, Real, Smaller, Between C & F, Perverted
2) 12 cm, Inverted, Real, Larger, Beyond C, Perverted, 1.5 cm
3) 35 in, -6.4 in, Inverted, Smaller, Real, Between C & F, Perverted
4) 75 cm, 1.67x
5) 13.3 cm, -1.3 cm, Inverted, Smaller, Real, Between C & F, Perverted
6) 12 cm, -3 times (or -3x), Inverted, Larger, Real, Beyond C, Perverted
7) 24 cm, Real
-30 cm, Virtual
8) -10 in, Upright, Virtual
9) -8.57 cm, 1.43 times (or 1.43x)
10) 80 cm
11) 20.16 cm, -8.1 cm, Inverted, Smaller, Real, Between C & F (but VERY close to F),
Perverted
12) c, a, b, a, g, c, h, i, e
13) 120 cm
14) 11.25 cm OR 18.75 cm
15) 3.33 cm