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