1. The problem statement, all variables and given/known data An object is 18 cm in front of a diverging lens that has a focal length of -12 cm. How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of 2.0 2. Relevant equations The thin lens equations: (1/di)+(1/do)=1/f The magnification equation (hi/ho)=-(di/do) f=focal length di=image distance do=object distance hi=image height ho=object height 3. The attempt at a solution The first thing I do is plug in values for the thin lens equations and solve for di (do and f are given). I end up getting: 18/di=-2.5 di=-7.2 cm So the distance of the image from the lens is -7.2 cm. However, this is where I get confused. I could use hi/ho=-(di/do) but there are two unknowns (hi/ho). The answer to this, by the way, is 48 cm. I don't know how to get to this, though.