Good vision depends on adequate intake of carotene-rich food. Select the best option from the following statements:
$(1)$ Vitamin $A$ derivatives are formed from carotene.
$(2)$ The photopigments are embedded in the membrane discs of the inner segment.
$(3)$ Retinal is a derivative of vitamin $A$.
$(4)$ Retinal is a light-absorbing part of all the visual photopigments.

• A
  $(1), (3)$ and $(4)$
• B
  $(1)$ and $(3)$
• C
  $(2), (3)$ and $(4)$
• D
  $(1)$ and $(2)$