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

Answer: (C)

For spherical mirror, $f = \frac{R}{2}$
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} $ or
$ u = f(1-\frac{1}{m})$
$u = -17.5 (1- \frac{1}{2.5})$
$= -17.5 \times (0.6) $
$= - 10.5\,cm$