Question

A concave shaving mirror has a radius of curvature of 35.0 cm. It is positioned so that the (upright) image of a man's 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

For spherical mirror, f = $f=\frac{R}{2}$

Given R = 35.0 cm or |f| = $\frac{35}{2}$ = 17.5 cm

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

Also magnification m = $\frac{-v}{u}$ or v = -mu

$\therefore \frac{1}{f}=\frac{1}{u}-\frac{1}{mu}oru=f(1-\frac{1}{m})$

$u=-17.5(1-\frac{1}{2.5})=17.5\times \left(0.6\right)=-10.5cm$