Prove that for a concave mirror, the radius of curvature is twice its focal length.

Draw a neat ray diagram for a concave mirror when an object is at C, and state the characteristics of image.

Draw ray diagram in each case to show the position and nature of the image formed when the object is placed between the pole P and focus F of a concave mirror.

Draw ray diagram in each case to show the position and nature of the image formed when the object is placed at $2\mathrm{F}$ of a convex lens.