A converging mirror forms a real image of height 4cm of an object of height 1cm placed 20cm away from the mirror:
- Calculate the image distance.
- What is the focal length of the mirror?
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$h_2=-4 cm \text { (real image) }$
$h_1=1 cm$
$u=-20 cm$
$\Rightarrow\frac{-4}{1}=-\frac{\text{v}}{-20}$
$\Rightarrow\text{v}=-80\text{cm}$
Image forms in front of the concave mirror.
$\frac{1}{-80}+\frac{1}{-20}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=-\frac{1}{80}-\frac{1}{20}=\frac{1-4}{80}=-\frac{5}{80}$
$\therefore\text{f}=-16\text{cm}$
$h_1=1 cm$
$u=-20 cm$
- v = ?
$\Rightarrow\frac{-4}{1}=-\frac{\text{v}}{-20}$
$\Rightarrow\text{v}=-80\text{cm}$
Image forms in front of the concave mirror.
- f = ?
$\frac{1}{-80}+\frac{1}{-20}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=-\frac{1}{80}-\frac{1}{20}=\frac{1-4}{80}=-\frac{5}{80}$
$\therefore\text{f}=-16\text{cm}$
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