What is the time difference between the actual sunset and the apparent sunset?

$(a)$ If a person wears a lens of power $-6\, D$ for distant vision and for correcting his near vision he needs a lens of $+2\, D$. Determine the focal length of the lenses in both the cases.
$(b)$ Give reasons for the following natural phenomena:
$(i)$ Stars twinkle.
$(ii)$ Planets do not twinkle.
$(iii)$ Stars appear raised in the sky.

Explain why the planets do not twinkle.

Which optical phenomenon is responsible for the formation of a mirage?

What is the twinkling of stars due to?

Is the position of a star as seen by us its true position? Justify your answer.