Draw ray diagrams showing the image formation by a convex lens when an object is placed:
$(a)$ Between optical centre and focus of the lens.
$(b)$ Between focus and twice the focal length of the lens.
$(c)$ At twice the focal length of the lens.
$(d)$ At infinity.
$(e)$ At the focus of the lens.

(N/A) To draw the ray diagrams for a convex lens,follow these steps for each case:
$(a)$ When the object is between the optical centre $(O)$ and focus $(F_1)$: The image is virtual,erect,and magnified,formed on the same side as the object.
$(b)$ When the object is between $F_1$ and $2F_1$: The image is real,inverted,and magnified,formed beyond $2F_2$ on the other side.
$(c)$ When the object is at $2F_1$: The image is real,inverted,and of the same size as the object,formed at $2F_2$.
$(d)$ When the object is at infinity: The image is real,inverted,and highly diminished (point-sized),formed at the focus $F_2$.
$(e)$ When the object is at the focus $F_1$: The image is real,inverted,and highly magnified,formed at infinity.