A boy of height 1.5m with his eye level at 1.4m stands before a plane mirror of length 0.75 m fixed on the wall. The height of the lower edge of the mirror above the floor is 0.8 m. Then ,

Options

A. the boy will see his full image
B. the boy cannot see his hair
C. the boy cannot see his feet
D. the boy can see neither his hair nor his feet.

Explanation

To solve the problem, we need to analyze the situation involving the boy, his eye level, and the plane mirror.

### Step-by-Step Solution:

1. **Identify the Height of the Boy and Eye Level**:
- The height of the boy is given as 1.5 meters.
- The eye level of the boy is at 1.4 meters.

2. **Determine the Position of the Mirror**:
- The lower edge of the mirror is positioned at a height of 0.8 meters above the floor.
- The length of the mirror is 0.75 meters.

3. **Visualize the Setup**:
- Draw a vertical line representing the wall with the mirror.
- Mark the height of the boy (1.5 m) and his eye level (1.4 m).
- Indicate the position of the mirror starting from 0.8 m to 1.55 m (0.8 m + 0.75 m).

4. **Calculate the Distance from Eye Level to the Bottom of the Mirror**:
- The distance from the boy's eye level (1.4 m) to the bottom of the mirror (0.8 m) is:
\[ 1.4 \, \text{m} - 0.8 \, \text{m} = 0.6 \, \text{m} \]

5. **Determine the Reflection Point**:
- The ray of light from the boy’s eyes will reflect off the mirror. The highest point of the mirror is at 1.55 m (0.8 m + 0.75 m).
- The ray will reflect downwards from the top edge of the mirror.

6. **Calculate the Maximum Height Visible in the Mirror**:
- Since the boy's eye level is at 1.4 m, and the mirror reflects light downwards, the highest point he can see in the mirror is at the height of the mirror (1.55 m).
- The distance from the boy's eye level to the top of the mirror is:
\[ 1.55 \, \text{m} - 1.4 \, \text{m} = 0.15 \, \text{m} \]

7. **Determine the Part of the Boy Not Visible**:
- The boy's total height is 1.5 m, and he can see up to 1.55 m in the mirror. However, since the ray reflects from the top edge, the lowest point he can see is determined by the reflection.
- The distance from the bottom of the mirror (0.8 m) to the boy's feet (0 m) is:
\[ 0.8 \, \text{m} - 0 \, \text{m} = 0.8 \, \text{m} \]
- Since the boy's eye level is at 1.4 m, he cannot see the part of his body below the line of sight to the mirror.

8. **Conclusion**:
- The boy cannot see his feet because the reflection only allows him to see up to 0.15 m above his eye level, which does not reach down to his feet.

### Final Answer:
The boy cannot see his feet in the mirror.