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An object is placed $30\,\text{cm}$ in front of a concave mirror of focal length $20\,\text{cm}$. The image distance from the mirror is:

A$+12\,\text{cm}$
B$-60\,\text{cm}$
C$+60\,\text{cm}$
D$-12\,\text{cm}$
Answer & Solution
Correct answer: B. $-60\,\text{cm}$
Using the standard sign convention, $u = -30\,\text{cm}$ and $f = -20\,\text{cm}$ for a concave mirror. The mirror formula $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ gives $\dfrac{1}{v} = \dfrac{1}{-20} - \dfrac{1}{-30} = -\dfrac{1}{60}$, so $v = -60\,\text{cm}$. The negative sign indicates the image is real and on the same side as the object, $60\,\text{cm}$ in front of the mirror.
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