The same Star Wars action figure, 8.0 cm tall, is placed 6.0 cm in front of a convex mirror with a focal length of -12.0 cm. Where is the image in this case, and what are the image characteristics?

Again, the first step is to draw a ray diagram. This should tell you that the image is located behind the mirror; that it is an upright, virtual image; that it is a little smaller than the object; and that the image is between the mirror and the focal point.

The second step is to confirm all those observations. The mirror equation gives:

di

=

do f do - f

=

6*(-12) 6 - -12

=

-72 18

= -4.0 cm

Solving for the magnification gives:

m

= -

di do

=

4.0 6.0

=

2 3

This gives an image height of (2/3) * 8 = 5.3 cm.

All of these results are consistent with the conclusions drawn from the ray diagram. The image is 5.3 cm high, virtual, upright compared to the object, and 4.0 cm behind the mirror.