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 do is the object distance in focal length, and Do is the object distance in centimeters,

do = Do/f

Similarly, if di is the image distance in focal lengths, and Di is the image distance in centimeters:

di = Di/f

This makes equation 1 become:

Hi = Ho/do (New equation 1)

Equation 2 becomes:

di = 1/do (New equation 2)


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:

di = 1/do

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