A toy is 14 cm in front of a convex spherical mirror. If the image of the toy is 5.8 cm behind the mirror, what is the focal length of the mirror?
A) -20 cm
B) -9.9 cm
C) -4.1 cm
D) +9.9 cm
E) +20 cm

Question

Quizplus · Accepted Answer

The mirror equation is $ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} $, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance. For a convex mirror, both $f$ and $v$ are considered negative in sign convention. Given $u = -14$ cm (since the object is in front of the mirror, it's taken as negative) and $v = +5.8$ cm (behind the mirror, but since it's a convex mirror, the image formed is virtual and thus considered positive in this context), we can solve for $f$. Plugging the values into the mirror equation gives $ \frac{1}{f} = \frac{1}{5.8} - \frac{1}{14} $, solving which gives $f \approx -9.9$ cm.

A Toy Is 14 Cm in Front of a Convex