Which of the following ray diagrams is correct for the ray of light incident on a lens shown in the figure?

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.

Which of the following always form a virtual image?

Write down the equation connecting the object distance,image distance,and focal length of lenses and mirrors.

How will you decide whether a given piece of glass is a convex lens,concave lens,or a plane glass plate?

Draw the ray diagram in each case to show the position,nature,and size of the image formed when the object is placed:
$(i)$ At the centre of curvature of a concave mirror.
$(ii)$ Within the focal length of a convex lens.
$(iii)$ Between the pole and focus of a concave mirror.
$(iv)$ In front of a convex mirror.
$(v)$ In front of a concave lens.