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

Answer

To solve the problem of how fast your image approaches you when a plane mirror is approaching you at a speed of 8 cm/s, we can follow these steps:

### Step 1: Understand the scenario
When you look into a plane mirror, the image you see is a virtual image that appears to be behind the mirror. The distance between you and your image is equal to the distance between you and the mirror.

### Step 2: Determine the speed of the mirror
The mirror is approaching you at a speed of 8 cm/s. This means that the distance between you and the mirror is decreasing at this rate.

### Step 3: Calculate the speed of the image
Since the image is located behind the mirror, when the mirror moves towards you, the image also moves towards you at the same rate. Therefore, the speed at which the image approaches you is equal to the speed of the mirror multiplied by 2 (because the distance to the image decreases from both the mirror and your position).

### Step 4: Apply the calculation
If the mirror is moving towards you at 8 cm/s, the image will approach you at:
\[ \text{Speed of image} = 2 \times \text{Speed of mirror} = 2 \times 8 \, \text{cm/s} = 16 \, \text{cm/s} \]

### Conclusion
Thus, the speed at which your image approaches you is 16 cm/s.

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