Magnification is the ratio of which of the following?

Write down the equation connecting the object distance,image distance,and focal length of lenses and mirrors.

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.

$A$ thin lens has a focal length of $-12\, cm$. Is it a convex lens or a concave lens?

$(a)$ Draw a ray diagram in each of the following cases to show the position and nature of the image formed when the object is placed:
$(i)$ between optical centre and principal focus $(F)$ of a convex lens.
$(ii)$ between $F$ and $2F$ of a convex lens.
$(iii)$ at $2F$ of a convex lens.
$(b)$ How will the nature and position of the image formed change in case $(i)$ and $(ii)$ in part $(a)$ of this question if the lens is replaced by a concave lens? Draw the corresponding ray diagram.

Which of the lenses with focal lengths $10 \, cm$,$20 \, cm$,$25 \, cm$,and $50 \, cm$ has the maximum power (in $, cm$)?