An object $4.0\,\text{cm}$ high is placed $25.0\,\text{cm}$ in front of a concave mirror of focal length $15.0\,\text{cm}$. At what distance from the mirror should a screen be placed to obtain a sharp image?
A$15.0\,\text{cm}$
B$25.0\,\text{cm}$
C$37.5\,\text{cm}$
D$40.0\,\text{cm}$
Answer & Solution
Correct answer: C. $37.5\,\text{cm}$
For a concave mirror, $u=-25\,\text{cm}$ and $f=-15\,\text{cm}$. Using $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ gives $\frac{1}{v}-\frac{1}{25}=-\frac{1}{15}$, so $\frac{1}{v}=-\frac{2}{75}$ and $v=-37.5\,\text{cm}$. A real image forms in front of the mirror, so the screen should be placed $37.5\,\text{cm}$ from the mirror.
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