The inverted image of a light bulb is formed on a screen located 9.00 m from a spherical mirror.The image is 4.00 times larger than the light bulb.Determine the object distance and the type of mirror used.
A)+0.444 m,concave
B)+2.25 m,concave
C)+36.0 m.concave
D)+0.0278 m,convex
E)+36.0 m,convex

Question

Quizplus · Accepted Answer

The magnification is given by $m=-\frac{q}{p}$, where $q$ is the image distance and $p$ is the object distance. Since the image is inverted, $m$ will be negative. We are given that $q=9.00	ext{ m}$ and $m=-4.00$, so we can solve for $p$:
$$m=-\frac{q}{p} \quad \Rightarrow \quad -4.00 = -\frac{9.00	ext{ m}}{p} \quad \Rightarrow \quad p=2.25	ext{ m}$$
The negative sign in $m$ indicates that the image is inverted, so the mirror must be concave since only concave mirrors can produce inverted images. Therefore, the correct choice is (B).

The Inverted Image of a Light Bulb Is Formed on a Screen