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  4. An object is 8 cm high. It is desired to form a real image 4 cm high at 60 cm from the mirror. The type of mirror needed with the focal length is

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Q. An object is $8\,cm$ high. It is desired to form a real image $ 4\,cm $ high at $ 60\,cm $ from the mirror. The type of mirror needed with the focal length is

J & K CETJ & K CET 2013Ray Optics and Optical Instruments

Solution:

$M=\frac{I}{O}=\frac{v}{u}$
Given, $O=8\, cm,\, I=4\, cm,\, v=60\, cm$
$\therefore \frac{4}{8}=\frac{60}{u}$
$\Rightarrow s u=120\, cm$
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{60}+\frac{1}{120}$
$\Rightarrow s t=40\, cm$ (convex)