A man 160 cm height stands in fromt of a plane mirror . His eyes are at a height of 150 cm from the floor. Then the minimum length of the plane mirror for him to see his full length image is -

Options

A. 85 cm
B. 170 cm
C. 80 cm
D. 340 cm

Answer

To find the minimum length of the plane mirror required for a man of height 160 cm to see his full image, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- The height of the man is 160 cm.
- The height of his eyes from the floor is 150 cm.
- We need to determine the minimum length of the mirror that allows him to see his full image.

2. **Visualize the Setup**:
- Draw a vertical line representing the plane mirror.
- Mark the height of the man (160 cm) and the height of his eyes (150 cm) on the diagram.

3. **Identify Key Points**:
- Let point A be the top of the man's head (160 cm).
- Let point B be the height of his eyes (150 cm).
- The bottom of the man (feet) is at 0 cm.

4. **Ray Diagram**:
- Draw a ray from the top of the man's head (point A) to the mirror, which reflects back to his eyes (point B).
- Draw another ray from the feet (0 cm) to the mirror, which also reflects back to his eyes (point B).

5. **Determine the Length of the Mirror**:
- The distance from the eyes to the top of the head (A) is 160 cm - 150 cm = 10 cm.
- The distance from the eyes to the feet (0 cm) is 150 cm - 0 cm = 150 cm.
- For the man to see his full image, the mirror must be at least half the distance from the eyes to the top of the head and half the distance from the eyes to the feet.

6. **Calculate the Minimum Length of the Mirror**:
- The minimum length of the mirror (L) can be calculated as:
\[ L = \frac{(Height of the man - Height of eyes) + (Height of eyes)}{2} \]
- Substituting the values:
\[ L = \frac{(10 \text{ cm}) + (150 \text{ cm})}{2} = \frac{160 \text{ cm}}{2} = 80 \text{ cm} \]

7. **Conclusion**:
- Therefore, the minimum length of the plane mirror required for the man to see his full length image is **80 cm**.