Question

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

• A. $60\, cm$
• B. $24\, cm$
• C. $-60\, cm$
• D. $-24 \,cm$

Answer 1

Answer: (C)

$-60\, cm$

Answer 2

When object before a concave mirror line within its focal length, its image is virtual, erect and on the other side. Since he wants his image to lie at $25 cm$ from him, it is $15 cm$ behind the mirror.

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{-10}+\frac{1}{15}=\frac{1}{f}$
$\Rightarrow \frac{-3+2}{30}=\frac{1}{f}$
$\Rightarrow f=-30\, cm$ (Concave mirror)
$R=2f=-60\, cm$