If an plane mirror approach towards you at a speed of v then the image also approach at same speed v. and the speed image relative to object will be 2v.
the plane mirror approach 10cm/s
so the image speed relative to you =2v
=2×10cm/s
=20cm/s
so the (3) 20cm/s is correct

Introduction:
When a plane mirror approaches an object, the image formed by the mirror also moves. The speed of the image depends on the relative speed between the object and the mirror. In this case, the plane mirror is approaching the observer at a speed of 10 cm/s. We need to determine the speed at which the image will approach the observer.

Explanation:
To find the speed of the image, we need to consider the following points:

1. Distance of the observer from the mirror:
The distance of the observer from the mirror is not given in the question. However, it is important to note that the image formed by a plane mirror is always at the same distance behind the mirror as the object is in front of it. Therefore, if the observer is at a distance of 'd' from the mirror, the object will also be at a distance of 'd' from the mirror.

2. Relative Speed:
The relative speed between the mirror and the observer is given as 10 cm/s. This means that the mirror is moving towards the observer at a speed of 10 cm/s.

3. Speed of Light:
The speed of light is a constant and is approximately 3 x 10^8 m/s. This means that light travels at a speed of 3 x 10^10 cm/s.

4. Speed of Image:
The speed of the image formed by the mirror can be calculated using the formula:

Speed of Image = Speed of Light / (Distance of Object + Distance of Image)

Since the distance of the object and the image from the mirror is the same, we can rewrite the formula as:

Speed of Image = Speed of Light / (2 x Distance of Object)

Calculation:
Let's assume that the observer is at a distance of 'd' from the mirror. Therefore, the distance of the object from the mirror is also 'd'.

Speed of Image = 3 x 10^10 cm/s / (2 x d)

Conclusion:
From the above calculation, we can conclude that the speed of the image formed by the plane mirror approaching the observer at a speed of 10 cm/s will be half the speed of light divided by the distance between the observer and the mirror. Therefore, the correct answer is option 3: 20 cm/s.