• # question_answer An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.

Answer:

 Given:   $u=-15\text{ }cm,\text{ }f=-10\text{ }cm,\,\,{{h}_{i}}=4\,cm$ Using the mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ $\frac{1}{v}-\frac{1}{15}=\frac{-1}{10}$ $\frac{1}{v}=\frac{-1}{10}+\frac{1}{15}$ $\frac{1}{v}=\frac{-15+10}{150}=\frac{-5}{150}$ $v=-30\,cm$ Thus, to obtain a sharp image of the object, the screen should be placed in front of the mirror at a distance of 30 cm. Now,            $m=\frac{-v}{u}=\frac{\text{height of image}}{\text{height of object}}$ $m=-\left( \frac{-30}{-15} \right)$$\Rightarrow m=-2$ $-2=\frac{{{h}_{1}}}{4}$ $\Rightarrow {{h}_{1}}=-8\,cm$ ‹         Height of the image is 8 cm.

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