When a beam of white light is passed through a prism,violet colour bends the most and red colour the least.

$A$ 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

$(a)$ 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.

$(a)$ What is meant by the least distance of distinct vision?
$(b)$ How does the thickness of the eye lens change when we shift our focus from a distant tree to reading a book?

$A$ near-sighted person can see only nearer objects.

Explain how a normal human eye is able to see distinctly objects placed at a distance as well as those placed at a nearer distance. What is the far point and near point of a normal human eye?