A man is 180 cm tall and his eyes are 10 cm below the top of his head. In order to see his entire height right from tow to head, he uses a plane mirror kept at a distance of 1 m from him. The minimum height of the plane mirror required is

Options

A. 180 cm
B. 90 cm
C. 85 cm
D. 170 cm

Answer

To find the minimum height of the plane mirror required for a man who is 180 cm tall to see his entire height from toe to head, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Height of the Man**:
The height of the man is given as 180 cm.

2. **Understand the Requirement for the Mirror**:
To see his entire height in a plane mirror, the minimum height of the mirror should be half of the man's height. This is a standard rule in optics.

3. **Calculate the Minimum Height of the Mirror**:
Using the formula:
\[ \text{Minimum Height of the Mirror} = \frac{\text{Height of the Man}}{2} \]
Substituting the height of the man:
\[ \text{Minimum Height of the Mirror} = \frac{180 \text{ cm}}{2} = 90 \text{ cm} \]

4. **Conclusion**:
Therefore, the minimum height of the plane mirror required for the man to see his entire height is **90 cm**.