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. 30 cm
• C. -24 cm
• D. 24 cm

Answer 1

The correct option is A 60 cm

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)

$\frac{1}{15}+\frac{1}{-10}=\frac{1}{f}$

$\frac{1}{f}=\frac{10-15}{150}\Rightarrow f=-30cm$

The radius of curvature is given as $R=2f=-60$ cm