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प्रश्न
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.
उत्तर
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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