$A$ spherical mirror forms an erect image of an object,three times the size of the object. If the distance between the object and the image is $80 \ cm$,then the focal length of the mirror is ......... $cm$.

An object is placed at a distance of $40 \ cm$ in front of a concave mirror of focal length $20 \ cm$. The image produced is

You are asked to design a shaving mirror assuming that a person keeps it $10\,cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25\,cm$. The radius of curvature of the mirror would then be.....$cm$.

$A$ spherical mirror forms an erect image three times the linear size of the object. If the distance between the object and the image is $80 \, cm$,the focal length of the mirror is........$cm$.

$A$ short object of length $L$ is placed along the principal axis of a concave mirror away from focus. The object distance is $u$. If the mirror has a focal length $f,$ what will be the length of the image? You may take $L << |u-f|$.

$A$ thin rod of length $f/3$ lies along the axis of a concave mirror of focal length $f$. One end of its magnified image touches an end of the rod. The length of the image is