The mirror equation is:
\[\frac{1}{f} = \frac{1}{u} + \frac{1}{v},\]
Here, \( f = +15 \, \text{cm} \) for a convex mirror, \( u = -10 \, \text{cm} \) is the object distance, and \( v \) represents the image distance.
Plugging in the known values yields:
\[\frac{1}{15} = \frac{1}{v} + \frac{1}{-10}.\]
Rearranging to solve for \( \frac{1}{v} \):
\[\frac{1}{v} = \frac{1}{15} + \frac{1}{10} = \frac{2 + 3}{30} = \frac{5}{30}.\]
Calculating the image distance:
\[v = \frac{30}{5} = +6 \, \text{cm}.\]
Consequently, the image is located 6 cm behind the mirror.
| Case | Mirror | Focal Length (cm) | Object Distance (cm) |
|---|---|---|---|
| 1 | A | 20 | 45 |
| 2 | B | 15 | 30 |
| 3 | C | 30 | 20 |