$A$ person can see distant sign boards clearly but cannot read clearly a book which is at $25\, cm$ from his eye. Giving reason,identify the defect. Draw a labelled ray diagram to illustrate this defect and its correction.

$A$ beam of white light falling on a glass prism gets split up into seven colours marked $1$ to $7$ as shown in the diagram. $A$ student makes the following statements about the spectrum observed on the screen.
$(a)$ The colours at position marked $3$ and $5$ are similar to the colour of the core of a hard-boiled egg and the colour of the sky respectively. Is the statement made by the student correct or incorrect? Justify.
$(b)$ Which of the two positions correspond closely to the colour of $(i)$ a solution of potassium permanganate,$(ii)$ danger or stop signal lights?

The danger signals installed at the top of tall buildings are red in colour. These can be easily seen from a distance because among all other colours, the red light

$A$ student sitting on the last bench can read the letters written on the blackboard but is not able to read the letters written in his textbook. Which of the following statements is correct?

How can we explain the reddish appearance of the Sun at sunrise or sunset? Why does it not appear red at noon?

$(a)$ 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?