A linear object AB of length $$5\text{ cm}$$ is placed along the principal axis of a convex mirror of radius of curvature $$20\text{ cm}$$. If A and B are 5 and $$10\text{ cm}$$ from the pole of the mirror, find the length of the image (in cm).

For the convex mirror $$f = +10\text{ cm}$$. For $$u = -5$$, $$\frac{1}{v} = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}$$, so $$v = \frac{10}{3}\text{ cm}$$. For $$u = -10$$, $$\frac{1}{v} = \frac{1}{10} + \frac{1}{10} = \frac{1}{5}$$, so $$v = 5\text{ cm}$$. The image length is $$5 - \frac{10}{3} = \frac{5}{3} \approx 1.67\text{ cm}$$.