## Fundamentals of Physics Extended (10th Edition)

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.