A man of height 1.6 m wishes to see his full image in a plane mirror. The minimum height of the mirror needed for this purpose is

Options

A. 3.2 m
B. 2.4 m
C. 1.6 m
D. 0.8 m

Answer

To determine the minimum height of a plane mirror required for a man of height 1.6 m to see his full image, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the minimum height of a mirror that allows a man who is 1.6 m tall to see his entire reflection.

2. **Concept of Reflection**: The image in a plane mirror is formed at the same distance behind the mirror as the object is in front of it. Therefore, to see his full image, the man needs to see both the top of his head and the bottom of his feet in the mirror.

3. **Height of the Mirror**: The height of the mirror required to see the full image is not the same as the height of the man. The mirror only needs to be half the height of the man.

4. **Deriving the Height of the Mirror**:
- Let the height of the man be \( H_m = 1.6 \, \text{m} \).
- The minimum height of the mirror \( H_{mirror} \) can be calculated using the formula:
\[ H_{mirror} = \frac{H_m}{2} \]
- Substituting the height of the man:
\[ H_{mirror} = \frac{1.6 \, \text{m}}{2} = 0.8 \, \text{m} \]

5. **Conclusion**: The minimum height of the mirror needed for the man to see his full image is \( 0.8 \, \text{m} \).

### Final Answer:
The minimum height of the mirror required is **0.8 m**.

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