**Examples for mirrors**

Example #1

Problem:

a.) An image is located at exactly the same
position as its object, for a mirror of focal length 6 *cm*. What is the object
distance?

Solution:

Use the formula with
* d_{i}* and

* d_{o }*=
12

b.) If the height of the object is 4.5 *mm*,
what is the height of the image?

Solution:

Use to see that the image height equals the object height.

* h_{i }*=
- 4.5

Example #2

Problem:

a.) A convex mirror has an
object 14 *cm *from the mirror, and the image appears to be 7 *cm* behind
the mirror. What is the focal length of the mirror?

Solution:

Use the formula with the image distance negative.

* f* = -14

b.) If the object height is
8.0 *mm*, what is the height of the image?

Solution:

Use the formula with the image distance negative.

* h_{i}* = 4.0

Example #3

Problem:

Suppose one wishes to
use a mirror as a projector, to illuminate a small object of height 1.0 *cm*, and display the image on a screen at a size of 1.0 *m*
where the distance to the screen is 4.0 *m*.

a.) What kind of mirror should one use? (concave or convex)

concave

b.) What should the focal length of the mirror be?

Solution: First calculate the object
distance via the magnification formula. One obtains: *d _{o}*

* f*
= 4.0