The spherical side mirror on a car is convex and has a radius of curvature of 25 cm.Another car is following,20 m behind the mirror.If the height of the car is 1.6 m,how tall is its image?
A) 5.0 cm
B) 2.0 cm
C) 4.0 cm
D) 3.0 cm
E) 0.99 cm

Question

Quizplus · Accepted Answer

The mirror equation for a convex mirror, where $f$ is the focal length, $u$ is the object distance, and $v$ is the image distance, is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$. The radius of curvature $R = 25$ cm, so the focal length $f = \frac{R}{2} = 12.5$ cm (remembering that for a convex mirror, the focal length is positive). The object distance $u = -2000$ cm (negative because it's real and in front of the mirror). Plugging these into the mirror equation gives $\frac{1}{12.5} = \frac{1}{v} - \frac{1}{2000}$. Solving for $v$ gives the image distance. The magnification $m = \frac{v}{u}$, and the height of the image $h_i = m \times h_o$, where $h_o = 160$ cm is the height of the object (the other car). Following through with the calculations, you find that the height of the image is approximately 0.99 cm, making E the correct answer.

The Spherical Side Mirror on a Car Is Convex and Has