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 determine whether the boy can see his head and feet in the mirror based on the given dimensions.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Height of the boy (H_boy) = 1.5 m
- Eye level of the boy (H_eye) = 1.4 m
- Length of the mirror (L_mirror) = 0.75 m
- Height of the lower edge of the mirror from the floor (H_lower_mirror) = 0.8 m

2. **Determine the Height of the Upper Edge of the Mirror:**
- The height of the upper edge of the mirror (H_upper_mirror) can be calculated as:
\[ H_{upper\_mirror} = H_{lower\_mirror} + L_{mirror} = 0.8\,m + 0.75\,m = 1.55\,m \]

3. **Check if the Boy Can See His Head:**
- The boy's head is at a height of 1.5 m.
- The upper edge of the mirror is at 1.55 m, which is higher than the height of the boy's head.
- Since the line of sight from the top of the boy's head to the mirror will reflect back to his eyes, he can see his head.

4. **Check if the Boy Can See His Feet:**
- The boy's feet are at a height of 0 m (floor level).
- The lower edge of the mirror is at 0.8 m.
- We need to see if the reflected ray from the feet can reach the boy's eyes.
- The incident ray from the feet to the mirror will reflect and must meet the boy's eye level (1.4 m).

5. **Using Similar Triangles:**
- The height from the floor to the lower edge of the mirror is 0.8 m.
- The distance from the lower edge of the mirror to the boy's eye level is:
\[ H_{eye} - H_{lower\_mirror} = 1.4\,m - 0.8\,m = 0.6\,m \]
- The distance from the feet to the lower edge of the mirror is 0.8 m.
- Using similar triangles, we can set up the ratio:
\[ \frac{H_{eye}}{Distance_{feet}} = \frac{H_{lower\_mirror}}{Distance_{eye\_level}} \]
\[ \frac{0.6}{0.8} = \frac{H_{lower\_mirror}}{Distance_{eye\_level}} \]
- Solving this gives us:
\[ H_{lower\_mirror} = \frac{0.6 \times 0.8}{0.8} = 0.6\,m \]
- Since the height of the boy's eyes (1.4 m) is lower than the height where the reflected ray would meet, he cannot see his feet.

6. **Conclusion:**
- The boy can see his head but cannot see his feet in the mirror.

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