If a virtual image is formed 14.5 cm along the principal axis from a convex mirror of focal length -19.5 cm,how far is the object from the mirror?
A)56.6 cm
B)14.5 cm
C)5.00 cm
D)20.0 cm
E)6.80 cm

Question

Quizplus · Accepted Answer

Using the mirror equation $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance. Substituting $f = -19.5$ cm and $v = -14.5$ cm (virtual image, hence negative), we solve for $u$. Rearranging gives $u = \frac{1}{\frac{1}{f} - \frac{1}{v}}$, leading to $u \approx 56.6$ cm.

If a Virtual Image Is Formed 14