Mirror and Magnification Equations

The Mirror EquationThe mirror equation allows you to locate the location of the image:

f = the distance from V to F** Note that f will be negative if the focal length is behind the mirror.

do = the distance from object to mirror

di = the distance from image to mirror** Note that di will be negative if the image is behind the mirror (virtual image).

Concave Mirror Convex Mirror

The Magnification Equation

• Tells you the change in size, or height (the magnification) of the image relative to the object using the object and image distances from the mirror.

• The magnification (m) is given by the formula:

m = magnification

ho = the height of the object

hi = the height of the image** Note that hi will be negative if the image is inverted (below the principal axis) compared to the object.

Summary of Mirror and Magnification Equations

• All distances are measured from the vertex of a curved mirror.

• Distances of real objects and images (in front of mirror) are positive.

• Distances of virtual objects and images (behind the mirror) are negative.

• Object and image heights are positive when measured above the principal axis and negative when measured below the principal axis.

When doing calculations...

• List the givens and required’s. • Show all of your work, including the formulas,

substituted values and final answer with a unit.

• A descriptive concluding statement is absolutely necessary.

Practice Problem 1A convex mirror has a focal length of −20 cm. An object with a height of 0.40 m is placed 30 cm from the mirror. a) Calculate the image distanceb) Calculate the image height

Givens:f = −20 cmho = 40 cmdo = 30 cm

Required:

a) di = ?

b) hi = ?

oi ddf

111

oi dfd

111

30

1

20

11

id

60

2

60

31

id

60

51

id

cmdi 12

605 id

The distance of the image is 12 cm. It is virtual and behind the mirror.

a)b)

o

i

o

i

d

d

h

h

30

)12(

40

ih

48030 ih

The height of the image is 16 cm. The image is upright.

cmhi 16

Practice Problem 1A concave mirror with a 12 cm focal length has a candle 2.5 cm tall placed in front of the mirror, 40 cm from the vertex. a) Calculate the image distance.b) What is the magnification of the image?

Givens:f = 20 cmho = 5 cmdo = 15 cm

Required:

a) di = ?

b) m = ?

oi ddf

111

oi dfd

111

025.008333.01

id

058333.01

id

058333.0

1di

cmdi 14.17

The distance of the image is about 17 cm. The image is real and in front of the mirror.

a) b)o

i

d

dm

40

)17(m

425.0m

Magnification is negative so image is inverted. It is 0.425 times smaller than object.

On your calculator, you can input 0.058333 and press 1/x to get the reciprocal