Find the focal length (in $cm$) of a convex mirror whose radius of curvature is $32\, cm$.

$A$ 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.

Define $1$ dioptre of power of a lens.

Name the type of mirror used in the following situation and support your answer with a reason:
$(a)$ Solar furnace

We wish to obtain an erect image of an object,using a concave mirror of focal length $15\, cm$. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

Name the mirror that can give an erect and enlarged image of an object.