1. Mirror and Magnification Equations

2. The Mirror Equation
The 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).
Convex Mirror
Concave Mirror

3. 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.

4. 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.

5. 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.

6. Practice Problem 1
A 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.
Calculate the image distance
Calculate the image height b) a)
Givens:
f = −20 cm
ho = 40 cm
do = 30 cm
Required:
a) di = ?
b) hi = ?
The distance of the image is 12 cm. It is virtual and behind the mirror.
The height of the image is 16 cm. The image is upright.

7. Practice Problem 1
A 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.
Calculate the image distance.
What is the magnification of the image? b) a)
Givens:
f = 20 cm
ho = 5 cm
do = 15 cm
Required:
a) di = ?
b) m = ?
The distance of the image is about 17 cm. The image is real and in front of the mirror.
Magnification is negative so image is inverted. It is times smaller than object.
On your calculator, you can input and press 1/x to get the reciprocal