# An Even Simpler Mathematical Relationship

You can get an even simpler mathematical relationship between the
object's size and location and the image's size and location if you
measure the object distance and image distance *in focal
lengths*. In other words, suppose that the focal length of a
converging mirror is 5 cm, and the object is located 15 cm from the
mirror's focus. The object distance is then 3 focal lengths (= 15
cm/5 cm). In other words, if d_{o} is the object distance in
focal length, and D_{o} is the object distance in
centimeters,
Similarly, if d_{i} is the image distance in focal
lengths, and D_{i} is the image distance in centimeters:

This makes equation
1 become:

(New equation 1)

Equation 2
becomes:

(New equation 2)

##

Example:

An object 5 cm tall is placed 2 focal lengths from
the focus of an converging mirror. What will be the size and
location of the resulting image?

From "new" equation 1, the height of the image will be:

From the "new" equation 2, the position of the image will be:

so the image will be located one-half focal length from the
mirror's focus. Easy, huh?

last update December 7, 2001 by JL
Stanbrough