Solution to 2008 Problem 74

We can use the mirror equation
\begin{align*}\frac{1}{d_0} + \frac{1}{d_i} = \frac{1}{f}\end{align*}
The focal length f for a convex mirror is half of the distance to the center of curvature and it is negative by convention. So, f = -R/2. If d_0 = R, then
\begin{align*}d_i = - \frac{R}{3}\end{align*}
where the negative sign indicates that the image is to the right of the mirror. Also, an image in a convex mirror is always upright. So, answer (E) is correct.

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