Answer
10.5 cm
Work Step by Step
Linear magnification, m= $-\frac{v}{u}$ = 2.50 where v is the image distance and u the object distance. This implies v= -2.50u.
Mirror equation tells us that
$\frac{1}{v}+\frac{1}{u}=\frac{2}{R}$ where R is the radius of curvature.
Substituting the value of v and R, we have
$\frac{1}{-2.50u}+\frac{1}{u}=\frac{2}{-35.0cm}$
Or
$\frac{1-2.50}{-2.50u}=\frac{2}{-35.0 cm}$
⇒ u=$ \frac{(1-2.50)(-35.0cm)}{2\times(-2.50)}$= -10.5 cm
So the distance between the mirror and the face is 10.5 cm.
