What kind of image is formed when an object is placed between the principal focus $(F)$ and the optical center $(O)$ of a convex lens?

Where should an object be placed in front of a convex lens to get a real image of the size of the object?

Where should an object be placed in front of a convex lens to obtain an image on the same side as the object?

Describe the different cases of image formation by a convex lens. Provide the ray diagram for each case.

An object $3.0 \text{ cm}$ high is placed perpendicular to the principal axis of a concave lens of focal length $7.5 \text{ cm}$. The image is formed at a distance of $5.0 \text{ cm}$ from the lens. Calculate $(i)$ distance at which object is placed,and $(ii)$ size and nature of image formed.

Where should an object be placed to use a convex lens as a simple microscope?