Question

An object $5\, cm$ tall is placed $1\, m$ from a concave spherical mirror which has a radius of curvature of $20 \,cm$. The size of the image is

• A. 0.11 cm
• B. 0.50 cm
• C. 0.55 cm
• D. 0.60 cm

Answer 1

Answer: (C)

0.55 cm

Answer 2

$h_{0}=5\, cm,\, h_{i}=$ ? $u=-100\, cm,\, R=-20\, cm.$ $\therefore f=-10\, cm$ Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ $\Rightarrow \frac{1}{1}-\frac{1}{100}=-\frac{1}{10}$ $\frac{1}{v}=\frac{1}{100}-\frac{1}{10}=\frac{1-10}{100}=-\frac{9}{100}$ $\therefore v=-\frac{100}{9}\, cm$ $\frac{h_{i}}{h_{0}}=\frac{y}{u}$ $\Rightarrow \frac{h_{i}}{5 cm }=\frac{(100 / 9)}{100}=\frac{1}{9}$ $\therefore h_{i}=5 / 9=0.55\, cm$