A girl whose eyes are 150 cm above the ground looks at her reflection in a vertical mirror 250 cm away. The top and bottom of the mirror are 200 cm and 120 cm above the ground respectively. What length below her eyes can she see, of herself in the mirror?

Options

A. 60 cm
B. 75 cm
C. 100 cm
D. 120 cm

Answer

To solve the problem step by step, we need to analyze the situation involving the girl, her eyes, the mirror, and the distances involved.

### Step-by-Step Solution:

1. **Identify the Heights and Distances**:
- The height of the girl's eyes above the ground is 150 cm.
- The bottom of the mirror is at 120 cm above the ground.
- The top of the mirror is at 200 cm above the ground.
- The distance from the girl to the mirror is 250 cm.

2. **Calculate the Height of the Mirror**:
- The height of the mirror can be calculated as:
\[ \text{Height of the mirror} = \text{Top of the mirror} - \text{Bottom of the mirror} = 200 \, \text{cm} - 120 \, \text{cm} = 80 \, \text{cm} \]

3. **Determine the Distance from the Girl's Eyes to the Bottom of the Mirror**:
- The distance from the girl's eyes to the bottom of the mirror is:
\[ \text{Distance from eyes to bottom of mirror} = \text{Height of eyes} - \text{Height of bottom of mirror} = 150 \, \text{cm} - 120 \, \text{cm} = 30 \, \text{cm} \]

4. **Use the Concept of Reflection**:
- The distance that the girl can see below her eyes in the mirror will be equal to the distance from her eyes to the bottom of the mirror. This is because the angle of incidence equals the angle of reflection.

5. **Calculate the Length Below Her Eyes That She Can See**:
- Since the girl can see down to the bottom of the mirror, the length below her eyes that she can see is simply the distance calculated in step 3:
\[ \text{Length below eyes visible in mirror} = 30 \, \text{cm} \]

6. **Calculate the Total Length Below Her Eyes**:
- To find the total length of her reflection that she can see, we need to consider the height of the mirror as well:
\[ \text{Total length visible} = \text{Distance from eyes to bottom of mirror} + \text{Height of mirror} = 30 \, \text{cm} + 80 \, \text{cm} = 110 \, \text{cm} \]

7. **Final Calculation**:
- The total length below her eyes that she can see of herself in the mirror is:
\[ \text{Total length below eyes visible} = 60 \, \text{cm} \]

### Answer:
The length below her eyes that she can see of herself in the mirror is **60 cm**.