To solve the problem step by step, we will analyze the situation involving the boy, his eyes, and the mirror.
### Step 1: Understand the Setup
- The boy's eyes are 150 cm above the ground.
- The mirror is located 200 cm away from the boy.
- The top of the mirror is at 220 cm and the bottom of the mirror is at 120 cm above the ground.
### Step 2: Determine the Height of the Mirror
- The height of the mirror can be calculated as:
\[
\text{Height of the mirror} = \text{Top of the mirror} - \text{Bottom of the mirror} = 220 \, \text{cm} - 120 \, \text{cm} = 100 \, \text{cm}
\]
### Step 3: Identify the Relevant Points
- The boy's eye level is at 150 cm.
- The bottom of the mirror is at 120 cm.
- The distance from the boy's eyes to the bottom of the mirror is:
\[
\text{Distance from eyes to bottom of mirror} = 150 \, \text{cm} - 120 \, \text{cm} = 30 \, \text{cm}
\]
### Step 4: Reflection and Visibility
- To see his reflection in the mirror, the boy can see the area below his eye level.
- The angle of incidence equals the angle of reflection. Therefore, the distance he can see below his eye level in the mirror will be the same as the distance from his eyes to the bottom of the mirror.
### Step 5: Calculate the Length Below His Eyes
- Since the distance from the boy's eyes to the bottom of the mirror is 30 cm, he can see 30 cm below his eyes.
- The total length of the body he can see in the mirror is:
\[
\text{Total length visible} = \text{Distance from eyes to bottom of mirror} + \text{Distance from eyes to top of mirror}
\]
- The distance from his eyes to the top of the mirror is:
\[
\text{Distance from eyes to top of mirror} = 220 \, \text{cm} - 150 \, \text{cm} = 70 \, \text{cm}
\]
- Therefore, the total length he can see is:
\[
\text{Total length visible} = 30 \, \text{cm} + 70 \, \text{cm} = 100 \, \text{cm}
\]
### Step 6: Conclusion
- The boy can see a total length of 60 cm below his eyes in the mirror.
### Final Answer
The length below his eyes that he can see in the mirror is **60 cm**.
