Q137 / 180 · AIIMS 2008 · Physics

An object \(5 \mathrm{~cm}\) tall is placed \(1 \mathrm{~m}\) from a concave spherical mirror which has a radius of curvature of \(20 \mathrm{~cm}\). The size of the image is

  • A
    \(0.11 \mathrm{~cm}\)
  • B
    \(0.50 \mathrm{~cm}\)
  • Correct answer
    C
    \(0.55 \mathrm{~cm}\)
  • D
    \(0.60 \mathrm{~cm}\).

Solution

$: h_0=5 \mathrm{~cm}, h_i=?$ $u=-100 \mathrm{~cm}, R=-20 \mathrm{~cm} . \quad \therefore f=-10 \mathrm{~cm}$ Using mirror formula, $\begin{aligned} & \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{v}-\frac{1}{100}=-\frac{1}{10} \\ & \frac{1}{v}=\frac{1}{100}-\frac{1}{10}=\frac{1-10}{100}=-\frac{9}{100} \\ & \therefore v=-\frac{100}{9} \mathrm{~cm} . \\ & \frac{h_i}{h_0}=\frac{v}{u} \Rightarrow \frac{h_i}{5 \mathrm{~cm}}=\frac{(100 / 9)}{100}=\frac{1}{9} \\ & \therefore \quad h_i=5 / 9=0.55 \mathrm{~cm} .\end{aligned}$

Hence, the correct answer is option: 'C'.

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