1. Initial position of image in a plane mirror

For a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it.

Given:

• Object distance from mirror $= 12\text{ cm}$

So initially, the image is formed $12\text{ cm}$ behind the mirror.

2. Mirror is moved towards the object

The mirror moves $4\text{ cm}$ towards the stationary object.

So the new object distance from the mirror becomes: $12 - 4 = 8\text{ cm}$

Hence, after moving, the image will be formed $8\text{ cm}$ behind the new position of the mirror.

3. Find the shift in image position

Let the initial mirror position be $M_1$ and final mirror position be $M_2$.

• Mirror moves $4\text{ cm}$ towards the object.
• In a plane mirror, image shifts by twice the displacement of the mirror when the object is stationary.

Therefore, $\text{Shift of image} = 2 \times 4 = 8\text{ cm}$

Now, since the mirror moved towards the object, the image also shifts in the same direction, i.e. towards the mirror's new position.

So the image shifts 8 cm towards the mirror.

4. Check options

• A: $4\text{ cm towards mirror}$ $\to$ Incorrect
• B: $2\text{ cm towards mirror}$ $\to$ Incorrect
• C: $8\text{ cm away from mirror}$ $\to$ Incorrect
• D: $8\text{ cm towards mirror}$ $\to$ Correct

Final Answer: $\boxed{\text{D: } 8\text{ cm towards mirror}}$