The distance between the object and its image formed by a plane mirror appears to be 24 cm. What is the distance between the mirror and the object?

Options

A. 24 cm
B. 12 cm
C. 36 cm
D. 48 cm

Explanation

To solve the problem, we need to find the distance between the mirror and the object when the distance between the object and its image formed by a plane mirror is given as 24 cm.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a plane mirror.
- Let the distance from the object (O) to the mirror (M) be denoted as \( OM \).
- The image (I) formed by the plane mirror will be at the same distance behind the mirror as the object is in front of the mirror.

2. **Relation Between Distances**:
- The distance from the object to the image can be expressed as:
\[ OI = OM + MI \]
- Since the image distance (MI) is equal to the object distance (OM) in the case of a plane mirror, we can write:
\[ OI = OM + OM = 2 \times OM \]

3. **Using the Given Information**:
- We know from the problem that the distance between the object and the image (OI) is 24 cm:
\[ OI = 24 \text{ cm} \]

4. **Setting Up the Equation**:
- Substituting the value of \( OI \) into our earlier equation:
\[ 24 = 2 \times OM \]

5. **Solving for OM**:
- To find \( OM \), divide both sides of the equation by 2:
\[ OM = \frac{24}{2} = 12 \text{ cm} \]

6. **Conclusion**:
- The distance between the mirror and the object (OM) is 12 cm.

### Final Answer:
The distance between the mirror and the object is **12 cm**.

---