A concave mirror produces a real image 1cm tall of an object 2.5mm tall placed 5cm from the mirror. Find the position of the image and the focal length of the mirror.
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$h _2=1 cm=10 mm$ (real image), $h _1=2.5 mm, u =-5 cm=-50 mm$,,$\text{m}=\frac{\text{h}_1}{\text{h}_2}$
$\text{m}=-\frac{10}{2.5}$
$\text{m}=-4$
and we know that
$\text{m}=-\frac{\text{v}}{\text{u}}$
$-4=-\frac{\text{v}}{(-50)}$
$\text{v}=200\text{mm}$
$\text{v}=200\text{cm}$
The image is formed 20cm in front of the mirror.
And
$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{-20}+\frac{1}{-5}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=\frac{-25}{100}$
$\text{f }=-4\text{cm}$
$\text{m}=-\frac{10}{2.5}$
$\text{m}=-4$
and we know that
$\text{m}=-\frac{\text{v}}{\text{u}}$
$-4=-\frac{\text{v}}{(-50)}$
$\text{v}=200\text{mm}$
$\text{v}=200\text{cm}$
The image is formed 20cm in front of the mirror.
And
$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{-20}+\frac{1}{-5}=\frac{1}{\text{f}}$
$\frac{1}{\text{f}}=\frac{-25}{100}$
$\text{f }=-4\text{cm}$
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