Why do stars twinkle?

Explain why stars twinkle while planets do not.

Which optical phenomenon is responsible for the twinkling of stars?

$(a)$ How does refraction take place in the atmosphere? Why do stars twinkle but not the planets?
$(b)$ State any two effects of atmospheric refraction on the sun as observed from the Earth.

$(a)$ 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.

Due to atmospheric refraction, the sun is visible about $2$ minutes before the actual sunrise and about $2$ minutes after the actual sunset. By how much time is the day lengthened due to this phenomenon?