The relation between the linear magnification $m$,the object distance $u$,and the focal length $f$ is:

Two objects $A$ and $B$ are placed at $15\,cm$ and $25\,cm$ from the pole in front of a concave mirror having a radius of curvature $40\,cm$. The distance between the images formed by the mirror is $..........\,cm$.

$A$ ray of light is incident on a convex mirror along a vector $3\hat i + 4\hat j + 12\hat k$. The normal to the convex mirror at the point of incidence is along $3\hat i + 4\hat j$. The unit vector along the reflected ray is:

An object placed in front of a concave mirror of focal length $0.15 \,m$ produces a virtual image,which is twice the size of the object. The position of the object with respect to the mirror is ........... $cm$. (in $.5$)

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.....$cm$.

An object is placed in front of a concave mirror of focal length $f$. $A$ virtual image is formed with a magnification of $2$. To obtain a real image of the same magnification,the object has to be moved by a distance of: