Question

An object $5cm$ tall is placed $1m$ from a concave spherical mirror which has a radius of curvature of $20cm$. 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)

$h_0=5cm,h_i=$ ?
$u=-100cm,R=-20cm.$
$\therefore f=-10cm$
Using mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{1}-\frac{1}{100}=-\frac{1}{10}$
$\frac{1}{v}=\frac{1}{100}-\frac{1}{10}=\frac{1-10}{100}=-\frac{9}{100}$
$\therefore v=-\frac{100}{9}cm$
$\frac{h_i}{h_0}=\frac{y}{u}$
$\Rightarrow \frac{h_i}{5cm}=\frac{(100/9)}{100}=\frac{1}{9}$
$\therefore h_i=5/9=0.55cm$