What is the role of the pupil in a human eye?

$A$ beam of white light falling on a glass prism gets split up into seven colours marked $1$ to $7$ as shown in the diagram.
$(a)$ The colours at positions marked $3$ and $5$ are similar to the colour of the sky and the colour of gold metal respectively. Is the above statement made by the student correct or incorrect? Justify.
$(b)$ Which of the above shown positions corresponds approximately to the colour of:
$(i)$ a brinjal
$(ii)$ danger signal
$(iii)$ neel (indigo) which is applied to clothes
$(iv)$ orange

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

$(i)$ What is the least distance of distinct vision for a normal eye?
$(ii)$ Does the above distance increase or decrease for a long-sighted eye (hypermetropia)? Give a reason for your answer with a diagram.

Why does the sky appear dark to passengers flying at high altitudes?

What is the range of clear vision for a person with normal vision?