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)

$10.5\,cm$

Answer 2

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 $u = f(1-\frac{1}{m})$ $u = -17.5 (1- \frac{1}{2.5})$ $= -17.5 \times (0.6)$ $= - 10.5\,cm$