Question

A concave shaving mirror has a radius of curvature of $35.0cm$. 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. $5.25cm$
• B. $21.0cm$
• C. $10.5cm$
• D. $42cm$

Answer 1

Answer: (C)

For spherical mirror, $f=\frac{R}{2}$
Given, $R=35.0cm$ or
$|f|=\frac{35}{2}=17.5cm$
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
$u=f(1-\frac{1}{m})$
$u=-17.5(1-\frac{1}{2.5})$
$=-17.5\times (0.6)$
$=-10.5cm$