Question 50 of 295

You are asked to design a shaving mirror assuming that a person keeps it at $10cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25cm$. The radius of curvature of the mirror would then be:

A$24cm$B$30cm$C$60cm$D$-24cm$

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Answer: (C) $60cm$

If $AB$ is the position of the face of man then $A'B'$ is the position of the image of a face. As the image is formed at $25cm$ from the object.$∴$ From concave mirror image is 15cm behind the mirror. So, $u=-10cm,v=+15cm$
$\Rightarrow \dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$$\Rightarrow \dfrac{1}{f}=\dfrac{1}{-10}+\dfrac{1}{15}=\dfrac{-3+2}{30}$
$\Rightarrow f=-30cm$. So, the radius of curvature,$=60cm$