Question

If an object 18 millimeters high is placed 12 millimeters from a spherical mirror, and the image is formed 4 millimeters in front of the mirror, what's the image's height?
Question 16 options:

A)

14 millimeters

B)

8 millimeters

C)

6 millimeters

D)

22 millimeters

Answer 1

To find the height of the image formed by the spherical mirror, we can use the magnification formula for mirrors:

\[
\text{Magnification} (m) = -\frac{h_i}{h_o} = \frac{d_i}{d_o}
\]

Where:
- \( h_i \) is the height of the image,
- \( h_o \) is the height of the object,
- \( d_i \) is the distance of the image from the mirror,
- \( d_o \) is the distance of the object from the mirror.

Given:
- \( h_o = 18 \) mm (height of the object),
- \( d_o = 12 \) mm (distance of the object from the mirror),
- \( d_i = -4 \) mm (distance of the image from the mirror; negative because it's in front of the mirror).

Now we can calculate the magnification using the distances:

\[
m = \frac{d_i}{d_o} = \frac{-4 \text{ mm}}{12 \text{ mm}} = -\frac{1}{3}
\]

Next, we can find the height of the image using the magnification and the height of the object:

\[
m = -\frac{h_i}{h_o}
\]
\[
-\frac{1}{3} = -\frac{h_i}{18 \text{ mm}}
\]

Now we can solve for \( h_i \):

\[
\frac{1}{3} = \frac{h_i}{18 \text{ mm}}
\]
\[
h_i = 18 \text{ mm} \times \frac{1}{3} = 6 \text{ mm}
\]

Thus, the height of the image is \( h_i = 6 \) mm.

The correct answer is:

**C) 6 millimeters**