Question

A convex mirror has a focal length of -0.5 m. An object is 2.0 m in front of the mirror. Where is the image formed?

Answer 1

We can find the image distance from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$d_i=\dfrac{1}{\dfrac{1}{f}-\dfrac{1}{d_o}},$$ $$d_i=\dfrac{1}{-\dfrac{1}{0.5\ m}-\dfrac{1}{2.0\ m}}=-0.4\ m.$$

The sign minus means that the image is virtual and located behind the mirror.