The correct option is (c).
Explanation
A convex lens is a converging lens that brings parallel rays of light to a focus. The nature, size, and orientation of the image formed depend on the distance of the object from the optical center of the lens.
Statement-wise Analysis:
- Statement 1 is Correct: A convex lens forms a real and inverted image for all object positions where the object is placed beyond the principal focus (i.e., object distance \(u > f\)). In these cases, light rays actually converge at a point after refraction.
- Statement 2 is Incorrect: A convex lens acts as a magnifying glass (simple microscope) only when the object is placed within the focal length (between the optical center and the focus). When the object is at infinity, the image formed is real, inverted, and highly diminished (point-sized) at the focus, which does not serve the purpose of magnification for viewing details.
- Statement 3 is Correct: When the object is placed very close to the lens (specifically, between the focus and the optical center), the refracted rays diverge. When extended backward, they form a virtual, erect, and magnified image. This is the principle behind the usage of a convex lens as a reading glass or magnifying glass.
Key Takeaway:
A convex lens forms a real and inverted image when the object is outside the focus, and a virtual, erect, and magnified image when the object is placed within the focal length.