Q142 / 160 · AP EAMCET 2023 (16 May Shift 2) · Physics
The image formed by a convex mirror of focal length $30 \mathrm{~cm}$ is a quarter of the size of the object. The distance of the object from the mirror is
- A$30 \mathrm{~cm}$
- Correct answerB$90 \mathrm{~cm}$
- C$120 \mathrm{~cm}$
- D$60 \mathrm{~cm}$
Solution
Focal length, $f=30 \mathrm{~cm}$
$\begin{aligned}
& \mathrm{m}=\frac{-\mathrm{v}}{\mathrm{u}}=\frac{1}{4} \\
& \mathrm{u}=-4 \mathrm{v} \\
& \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{v}}-\frac{1}{4 \mathrm{v}}=\frac{4-1}{4 \mathrm{v}} \\
& \frac{1}{\mathrm{f}}=\frac{3}{4 \mathrm{v}} \\
& \mathrm{f}=\frac{4 \mathrm{v}}{3} ; \frac{30 \times 3}{4}=\mathrm{v} \\
& \mathrm{u}=\frac{-4 \times 30 \times 3}{4}=-90 \mathrm{~cm}
\end{aligned}$
Hence, the correct answer is option: 'B'.