A plane mirror is approaching you at a speed of `10cm//sec`. You can see your image in it. At what speed will your image approach you?

Options

A. `10cm//sec`
B. `5 cm//sec`
C. `20cm//sec`
D. `15cm//sec`

Explanation

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

### Step 1: Understand the motion of the mirror and the image
A plane mirror reflects light and creates an image that appears to be behind the mirror. When the mirror moves towards you, the image also moves towards you, but at a different speed.

### Step 2: Identify the speed of the mirror
The speed of the plane mirror is given as \(10 \, \text{cm/s}\).

### Step 3: Determine the relationship between the speed of the mirror and the speed of the image
When a plane mirror moves towards an observer, the image approaches the observer at twice the speed of the mirror. This is because the distance between the observer and the image decreases as the mirror approaches.

### Step 4: Calculate the speed of the image
Since the speed of the mirror is \(10 \, \text{cm/s}\), the speed of the image approaching you will be:
\[ \text{Speed of the image} = 2 \times \text{Speed of the mirror} = 2 \times 10 \, \text{cm/s} = 20 \, \text{cm/s} \]

### Step 5: Conclusion
The speed at which your image approaches you is \(20 \, \text{cm/s}\).

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