Which phenomenon is responsible for the blue color of the clear sky?

Why does it take some time to see objects in a cinema hall when we just enter the hall from bright sunlight? Explain in brief.

If the size of the scattering particles is large,which color of light do they scatter?

The far point of a myopic person is $40 \, cm$. What type of lens should they wear to see distant objects clearly? Calculate the focal length and the power of the lens they should use.

$A$ 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?

Define dispersion of white light.