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

Which optical phenomenon is responsible for the twinkling of stars?

Due to atmospheric refraction of light,the Sun appears to rise $................$ its actual sunrise.

$(a)$ 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.

$(a)$ With the help of a suitable diagram,explain why the Sun is visible to us two minutes before the actual sunrise and two minutes after the actual sunset.
$(b)$ Name the phenomenon responsible for the apparent flattening of the Sun's disc at sunrise and sunset.