Option 1 states that an object placed in front of a convex mirror will never form an inverted image. A convex mirror always produces a virtual image, which means that the image formed appears to be behind the mirror and is always upright. This is because the reflected rays diverge after hitting the mirror, resulting in an image that appears smaller than the actual object.

Option 2 states that the image moves towards the focus when the object moves towards the mirror. This statement is incorrect as the position of the image formed by a convex mirror is not affected by the movement of the object. The image will always be virtual, upright, and located behind the mirror.

Option 3 states that depending on the position of the object with respect to the mirror, the image can be inverted and real. This statement is incorrect for a convex mirror. A convex mirror always produces a virtual image which is upright and appears to be behind the mirror.

Option 4 states that the size of the image becomes larger than that of the object when the object is placed at a distance equal to half the focal length. This statement is incorrect as a convex mirror always produces an image that is smaller than the object, regardless of the object`s position.

Alert - The correct answer should be Option 3.