A concave mirror forms an image of 20cm high object on a screen placed 5.0m away from the mirror. The height of the image is 50cm. Find the focal length of the mirror and the distance between the mirror and the object.
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Given that,
$H_1 = 20cm, v = -5m = -500cm, h_2 = 50cm$
Since, $\frac{-\text{v}}{\text{u}}=\frac{\text{h}_2}{\text{h}_1}$
or $\frac{500}{\text{u}}=-\frac{50}{20}$ (because the image in inverted)
or $\text{u}=-\frac{500\times2}{5}=-200\text{cm}=-2\text{m}$
$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$ or $\frac{1}{-5}+\frac{1}{-2}=\frac{1}{\text{f}}$
or $\text{f}=\frac{-10}{7}=-1.44\text{m}$
So, the focal length is 1.44m.
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