The focal length of a concave mirror is $20 \ cm$. Determine where an object must be placed to form an image,magnified two times and real.

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

What will be the height of the image when an object of height $2 \ mm$ is placed on the principal axis of a convex mirror (of radius of curvature $40 \ cm$) at a distance of $20 \ cm$ from the mirror?

$A$ thin cylindrical rod of length $10\,cm$ is placed horizontally on the principal axis of a concave mirror of focal length $20\,cm$. The rod is placed in such a way that the midpoint of the rod is at $40\,cm$ from the pole of the mirror. The length of the image formed by the mirror will be $\frac{x}{3}\,cm$. The value of $x$ is $............$.

$A$ concave shaving mirror has a radius of curvature of $35.0 \, cm$. It is positioned so that the upright image of a man's face is $2.5 \, times$ the size of the face. How far is the mirror from the face in $cm$?

$A$ concave mirror of focal length $f$ produces a real image $n$ times the size of the object. The magnitude of the distance of the object from the mirror is: