Question

A concave shaving mirror has a radius of curvature of 35.0 cm. It is positioned so that the (upright) image of a mans face is 2.50 times the size of the face. How far is the mirror from the face?

• A. 5.25 cm
• B. 21.0 cm
• C. 10.5 cm
• D. 42 cm

Answer 1

The correct option is C 10.5 cm

Radius of curvature$=35cm$

Focal length$=\frac{35}{2}cm$

Given ,

$\frac{heightofimage}{heightofobject}=\frac{-v}{u}=2.5$

$-v=2.5u\Rightarrow v=\frac{-25}{10}u$

For a mirror,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{10}{-25u}+\frac{1}{u}=\frac{2}{35}$

$\Rightarrow \frac{1}{u}(1-\frac{10}{25})=\frac{2}{35}$

$\Rightarrow u=\frac{25-10}{25}\times \frac{35}{2}=u$

$u=\frac{15\times 35}{25\times 2}=\frac{21}{2}cm$

$u=10.5cm$