Convex mirrors are often used in side-view mirrors on trucks.Such mirrors often warn "Objects in mirror are closer than they appear." Assume a convex mirror has a radius of curvature of 12.0 m and that there is a car that is 14.0 m behind the mirror.Find the magnitude of the distance between the mirror and the image of the car.

Question

Quizplus · Accepted Answer

The mirror equation for a convex mirror, where the image distance ($v$), object distance ($u$), and radius of curvature ($R$) are related, is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where $f = \frac{R}{2}$. Given $R = 12.0 m$, $f = 6.0 m$, and $u = -14.0 m$ (object distance is taken as negative in mirror equation convention), we can find $v$. Substituting $f$ and $u$ into the mirror equation gives $\frac{1}{6.0} = \frac{1}{v} - \frac{1}{14.0}$. Solving for $v$ yields $v = 4.2 m$, indicating the image is formed 4.2 meters behind the mirror.

Convex Mirrors Are Often Used in Side-View Mirrors on Trucks