A plane mirror is approaching you at 8 cm/s. You are able to see your image in it. At what speed will your image approach you?

Options

A. 4 cm/s
B. 8 cm/s
C. 16 cm/s
D. 24 cm/s

Explanation

To solve the problem of how fast your image in a plane mirror approaches you when the mirror is moving towards you, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- You are standing in front of a plane mirror.
- The mirror is moving towards you at a speed of 8 cm/s.

2. **Determine the Speed of the Image**:
- When a plane mirror moves towards an observer, the image in the mirror also moves towards the observer.
- The speed of the image relative to the observer is double the speed of the mirror.

3. **Calculate the Speed of the Image**:
- Since the mirror approaches you at 8 cm/s, the speed of the image will be:
\[ \text{Speed of Image} = 2 \times \text{Speed of Mirror} \]
\[ \text{Speed of Image} = 2 \times 8 \text{ cm/s} = 16 \text{ cm/s} \]

4. **Conclusion**:
- Therefore, the speed at which your image approaches you is 16 cm/s.

### Final Answer:
The image will approach you at a speed of **16 cm/s**.

---