A cell phone that is $8.90 \mathrm {~cm}$ tall is placed in front of a convex mirror. The image of the phone is $7.80 \mathrm {~cm}$ tall and is located $14.8 \mathrm {~cm}$ from a mirror. What is the mirror's focal length?
A) $+ 120 \mathrm {~cm}$
B) $- 105 \mathrm {~cm}$
C) $- 120 \mathrm {~cm}$
D) $+ 16.9 \mathrm {~cm}$
E) $- 13.0 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The image is virtual and upright, so the mirror is convex. The magnification is:$$m = \frac{h_i}{h_o} = \frac{-7.80 \mathrm {~cm}}{8.90 \mathrm {~cm}} = -0.876$$The magnification equation is:$$m = \frac{d_i}{d_o}$$where $d_i$ is the image distance and $d_o$ is the object distance. Substituting the given values, we get:$$-0.876 = \frac{14.8 \mathrm {~cm}}{d_o}$$Solving for $d_o$, we get:$$d_o = -16.9 \mathrm {~cm}$$The focal length is given by:$$f = \frac{d_i d_o}{d_i + d_o}$$Substituting the given values, we get:$$f = \frac{(14.8 \mathrm {~cm})(-16.9 \mathrm {~cm})}{14.8 \mathrm {~cm} - 16.9 \mathrm {~cm}} = -120 \mathrm {~cm}$$Therefore, the correct answer is C.

A Cell Phone That Is 8.90 cm8.90 \mathrm {~cm}8.90 cm Tall Is Placed in Front of a Convex Mirror

A Cell Phone That Is $8.90 \mathrm {~cm}$ Tall Is Placed in Front of a Convex Mirror