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Question
A concave mirror forms an image of 20 cm high object on a screen placed 5.0 m away from the mirror. The height of the image is 50 cm. Find the focal length of the mirror and the distance between the mirror and the object.
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Solution
Given,
Height of the object, h1 = 20 cm,
Distance of image from screen v = −5.0 m = −500 cm,
\[- \frac{v}{u} = \frac{h_2}{h_1}\]
\[or \frac{- ( - 500)}{u} = \frac{50}{20}\]
Where 'u' is the distance of object from screen.
(As the image is inverted)
Using mirror formula,
\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]
\[or \frac{1}{- 5} + \frac{1}{- 2} = \frac{1}{f}\]
\[or - \frac{1}{f} = \frac{7}{10}\]
\[or f = - \frac{10}{7} = - 1 . 44 \text{ m }\]
Hence, the required focal length of the concave mirror is 1.44 m.
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