The correct option is (a).
Explanation
Image formation by a plane mirror is governed by the laws of reflection. The image produced is virtual, erect, laterally inverted, and of the same size as the object. A defining characteristic of plane mirrors is the specific geometric relationship between the position of the object and the position of the image relative to the reflecting surface.
Statement-wise Analysis:
- Statement 1 is Correct: In a plane mirror, the image is formed at a distance behind the mirror that is exactly equal to the distance of the object in front of it. Mathematically, object distance ($u$) is equal to image distance ($v$).
- Statement 2 is Incorrect: Because the image distance is always equal to the object distance, any change in the object's position results in a corresponding change in the image's position. If an object is moved closer to the mirror, the image also appears to move closer to the back of the mirror. It does not move farther away.
Key Takeaway:
For a plane mirror, the distance of the image behind the mirror is always equal to the distance of the object in front of the mirror ($u = v$). Consequently, the image mimics the movement of the object relative to the mirror surface.