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: (A)

The mirror formula is given as $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ ... (i)
The position of object is $10\, cm$ left of mirror and position of image is
$25-10=15\, cm$ right of mirror
$u =-10\, cm$ and $v =15\, cm$ substituting values in equation (i)
$\frac{1}{15}+\frac{1}{-10}=\frac{1}{ f }$
$\frac{1}{f}=\frac{10-15}{150}$
$\Rightarrow f=-30\, cm$
The radius of curvature is given as
$R=2 f=-60\, cm$