How far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly$\frac{1}{4}$ th the size of the object?
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f = -20cm, $\text{m}=-\frac{1}{4}$ (real image)$\text{m}=-\frac{\text{v}}{\text{u}}$
$-\frac{1}{4}=-\frac{\text{v}}{\text{u}}$
$\text{u}=4\text{v}$
so$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{\text{v}}+\frac{1}{\text{4v}}=\frac{1}{(-20)}$
$\frac{5}{\text{4v}}=-\frac{1}{20}$
$\frac{1}{\text{v}}=\frac{100}{4}=25\text{cm}$
$\therefore\text{u}=4\text{v}$
$\text{u}=4(-25)$
$=-100\text{cm}$
The object should be palced 100cm to the left of the mirror.
$-\frac{1}{4}=-\frac{\text{v}}{\text{u}}$
$\text{u}=4\text{v}$
so$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{\text{v}}+\frac{1}{\text{4v}}=\frac{1}{(-20)}$
$\frac{5}{\text{4v}}=-\frac{1}{20}$
$\frac{1}{\text{v}}=\frac{100}{4}=25\text{cm}$
$\therefore\text{u}=4\text{v}$
$\text{u}=4(-25)$
$=-100\text{cm}$
The object should be palced 100cm to the left of the mirror.
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