# Question #2d93b

May 15, 2014

The equation used to relate object distance (${d}_{o}$), image distance (${d}_{i}$), and focal length ($f$)for a spherical mirror is:

$\frac{1}{{d}_{o}} + \frac{1}{{d}_{i}} = \frac{1}{f}$

With convex mirrors, you must be careful because the focal length of the mirror is negative because it is behind the mirror. Also, you must make sure to have all your distances in the same units (here convert all the distances to meters).

$\frac{1}{5 m e t e r s} + \frac{1}{{d}_{i}} = \frac{1}{- 0.1 m e t e r s}$

So $\frac{1}{{d}_{i}} = - \frac{51}{5} = - 10.2$ which means that ${d}_{i} = \frac{1}{-} 10.2 = - 0.098$ meters.

The fact that the image distance is negative means that the image is formed behind the mirror, which will always be true for a convex mirror.

Here is a link to a video showing how to do this (note that he uses s for ${d}_{o}$ and s' for ${d}_{i}$ and uses an equation that comes from rearranging the equation that I gave above):