An object is 10. cm from the mirror, its height is 3.0 cm, and the focal length is 2.0 cm. what is the image height? (indicate the object orientation by including the + or - sign with the answer.)

We know distance of the object from the lens D0=10 cm, height of the object H0=3 cm, focal length f=2 cm and we want to know the image height Hi. 

First we have to calculate the distance of the image Di from the lens using the lens equation:

(1/f)=(1/D0)+(1/Di)

(1/Di)=(1/f)-(1/D0)=(1/2)-(1/10)=4/10

Di=10/4=2.5 cm. 

Now we can calculate height of the image Hi from the magnification formula: 

M=-(Di/D0)=(Hi/H0)

Hi={-(Di/D0)}*H0={-(2.5/10)*3}=-0.75 cm. 

So height of the image is Hi=-0.75 cm. The minus sign tells us the image is inverted.