$A$ spherical mirror and a thin spherical lens have each a focal length of $-15\,cm$. The mirror and the lens are likely to be

Name the type of mirror used in the following situation.
Support your answer with a reason.
$(a)$ Headlights of a car

$A$ concave mirror produces a three times magnified (enlarged) real image of an object placed at $10 \, cm$ in front of it. Where is the image located (in $cm$)?

$A$ 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 convex lens if the image is equal to the size of the object? Also,find the power of the lens.

Find the power of a concave lens of focal length $2 \,m$ in $Diopter$.

An object of size $7.0\, cm$ is placed at $27\, cm$ in front of a concave mirror of focal length $18\, cm$. At what distance from the mirror should a screen be placed,so that a sharp focussed image can be obtained? Find the size and the nature of the image.