A convex mirror with a radius of curvature of 10 cm (C=10 cm) produces a virtual image 1/3 the size of the real object. What is the object's distance?

Answer 1

The mirror's focal length is
f = -R/2 = -5 cm.
The minus sign is there because it is convex.

The basic imaging equation is:

1/Do + 1/Di = 1/f = -1/5
and the magnification ratio is Di/Do = -1/3

1/Do -3/Do = -1/5

2/Do = 1/5
Do = 10 cm is the object distance