$A$ candle is placed at a distance of $10 \ cm$ from a plane mirror. At what distance from the mirror will the image of this candle be formed (in $cm$)?

Define the term principal focus for a convex mirror.

$(a)$ Define power of a lens and write its $SI$ unit.
$(b)$ $A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from it. Where is the needle placed in front of the lens, if the image size is equal to the object size? Also, find the power of the lens.

Copy the given figure and complete it to show the formation of the image of the object $AB$. Name the lens used in the figure.

Is it possible for a lens to act as a convergent lens in one medium and a divergent lens in another?

$A$ concave mirror and a convex lens are held in water. What changes, if any, do you expect in their focal length?