Give the mathematical expression for the power of a lens.

When does Snell's law fail?

Two plane mirrors are at right angles to each other. $A$ man stands between them and combs his hair with his right hand. In how many images will he be seen using his left hand?

$A$ pencil when dipped in water in a glass tumbler appears to be bent at the interface of air and water. Will the pencil appear to be bent to the same extent,if instead of water we use liquids like kerosene or turpentine? Support your answer with reason.

State the laws of refraction.

$A$ student focussed the image of a candle flame on a white screen using a convex lens. He noted down the position of the candle,screen,and the lens as under:
Position of candle $= 12.0\, cm$
Position of convex lens $= 50.0\, cm$
Position of the screen $= 88.0\, cm$
$(i)$ Where will the image be formed if he shifts the candle towards the lens at a position of $31.0\, cm$?
$(ii)$ What will be the nature of the image formed if he further shifts the candle towards the lens?
$(iii)$ Draw a ray diagram to show the formation of the image in case $(ii)$ as said above.