An object is in front of a concave spherical mirror, and its image is 4.0 cm behind the mirror. If the focal length of the mirror has a magnitude of 5.0 cm, where is the object?
A) 9.0 cm in front of the mirror
B) 1.0 cm behind the mirror
C) 2.2 cm in front of the mirror
D) 2.2 cm behind the mirror

Question

Quizplus · Accepted Answer

The mirror equation, $ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance, can be used to find the object distance. Given $f = -5.0 \, \text{cm}$ (concave mirror focal lengths are negative) and $d_i = -4.0 \, \text{cm}$ (images formed behind a mirror are considered to have negative image distances), we can solve for $d_o$. Plugging in the values, we get $ \frac{1}{-5.0} = \frac{1}{d_o} - \frac{1}{4.0} $, solving for $d_o$ gives approximately $2.2 \, \text{cm}$, indicating the object is in front of the mirror.

An Object Is in Front of a Concave Spherical Mirror