Question

A convex mirror with a radius of curvature of
48.6 cm forms a 1.66 cm tall image of a pencil
at a distance of 13.2 cm behind the mirror.
a) Find the object distance for the pencil.
Answer in units of cm

Answer 1

To find where the object is, we use the following formula:\[\frac{ 1 }{ s _{i} }=\frac{ 1 }{ s _{o} }+\frac{ 1 }{ f }\]where si is the image distance; so is the object distance; and f is the focal length.

Note the following conventions:
1. Light travels from left to right.
2. Distances to the left of the mirror are negative.
3. Distances to the right of the mirror are positive.
4. For reflective or refractive surfaces, the surface's radius of curvature is measured from the center of curvature to the surface.

The focal length of a reflective surface is given by:\[f=\frac{ R }{ 2 }\]where f is the focal length; and R is the mirror's radius of curvature. This means for the convex surface in this problem, the radius of curvature is measured from right to left, meaning it's radius of curvature, R, is negative.