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)

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