For a convex mirror of radius of curvature $3.00\,\text{m}$, an object is placed $5.00\,\text{m}$ in front of the mirror. Where is the image formed?
A$+1.15\,\text{m}$ behind the mirror
B$-1.15\,\text{m}$ in front of the mirror
C$+3.00\,\text{m}$ behind the mirror
D$-5.00\,\text{m}$ in front of the mirror
Answer & Solution
Correct answer: A. $+1.15\,\text{m}$ behind the mirror
For a convex mirror, $f=R/2=+1.5\,\text{m}$ and $u=-5.0\,\text{m}$. Using $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ gives $\frac{1}{v}-\frac{1}{5}=\frac{2}{3}$, so $\frac{1}{v}=\frac{13}{15}$ and hence $v=\frac{15}{13}\approx +1.15\,\text{m}$. The positive sign shows the image is formed behind the mirror.
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