Find the minimum height of a mirror where one can see his full image.

Answer

To find the minimum height of a mirror required for a person to see their full image, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Reflection**:
When light reflects off a mirror, the angle of incidence equals the angle of reflection. This means that the light from the top of the object (the person) must reach the mirror and then reflect back to the eyes of the observer.

2. **Identify the Height of the Object**:
Let’s denote the height of the person (the object) as \( h \).

3. **Determine the Required Height of the Mirror**:
For a person to see their full image in the mirror, the mirror must be positioned such that it reflects light from both the top of the person's head and their feet back to their eyes.

4. **Calculate the Minimum Height of the Mirror**:
The minimum height of the mirror required can be derived from the geometry of the situation. The distance from the eyes to the top of the head and the feet must be equal when reflected. Therefore, the minimum height of the mirror \( h_m \) is given by:
\[ h_m = \frac{h}{2} \]
This means that the mirror needs to be at least half the height of the person.

5. **Example Calculation**:
If the height of the person is \( 6 \) meters, then the minimum height of the mirror would be:
\[ h_m = \frac{6}{2} = 3 \text{ meters} \]

### Final Answer:
The minimum height of the mirror required for a person to see their full image is half of their height.