$(a)$ Draw a ray diagram in each of the following cases to show the position and nature of the image formed when the object is placed:
$(i)$ between optical centre and principal focus $(F)$ of a convex lens.
$(ii)$ between $F$ and $2F$ of a convex lens.
$(iii)$ at $2F$ of a convex lens.
$(b)$ How will the nature and position of the image formed change in case $(i)$ and $(ii)$ in part $(a)$ of this question if the lens is replaced by a concave lens? Draw the corresponding ray diagram.

(N/A) For the ray diagrams of a convex lens:
$(i)$ When the object is between the optical centre and the principal focus $(F)$,the image formed is virtual,erect,and magnified,and it is formed on the same side of the lens as the object.
$(ii)$ When the object is between $F$ and $2F$,the image formed is real,inverted,and magnified,and it is formed beyond $2F$ on the other side of the lens.
$(iii)$ When the object is at $2F$,the image formed is real,inverted,and of the same size as the object,and it is formed at $2F$ on the other side of the lens.
$(b)$ If the convex lens is replaced by a concave lens,the nature and position of the image will change as follows:
In both cases $(i)$ and $(ii)$,the concave lens will always form a virtual,erect,and diminished image. The image will always be formed between the optical centre and the principal focus $(F)$ on the same side as the object,regardless of the object's position.