What will be the focal length of a lens whose power is given as $+2.0 \ D$?

$A$ 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.

$A$ $10 \, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $30 \, cm$. The distance of the object from the lens is $20 \, cm$. Find the $(i)$ position,$(ii)$ nature,and $(iii)$ size of the image formed.

An object $5\, cm$ high is kept $25\, cm$ away from a converging lens (convex lens) of focal length $10\, cm$. What is the nature,position,and size of the image?

Where should an object be placed in front of a convex lens to obtain an image on the same side as the object?

What is meant by power of a lens? Define its $SI$ unit. You have two lenses $A$ and $B$ of focal lengths $+10\, cm$ and $-10\, cm$ respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed $8\, cm$ from the lens? Draw a ray diagram to justify your answer.