Draw ray diagrams to show focus for a concave mirror

Draw ray diagrams to show focus for a Convex mirror.

Draw ray diagrams to show the principal focus of converging (or convex) lens

Draw ray diagrams to show the principal focus of diverging (or concave) lens.

An object is placed at a distance X_1 from the focus of a concave mirror, Its real image is formed at a distance X_2 from the focus, Show that the focal length of the mirror is sqrt(x_1x_2)

Draw a ray diagram to show the virtual image formed due to reflection from a concave mirror.