$A$ convex mirror of focal length $f$ forms an image which is $\frac{1}{n}$ times the size of the object. The distance of the object from the mirror is

$A$ driving mirror consists of a cylindrical mirror of radius of curvature $10 \,cm$ and the length over the curved surface is $10 \,cm$. If the eye of the driver is assumed to be at a great distance from the mirror,then the field of view in radians is: (in $.0$)

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.....$cm$.

Where should an object be placed in front of a concave mirror of focal length $20\,cm$ so that the image is $2\,times$ the size of the object?

At what distance in front of a concave mirror of focal length $30\; cm$,should an object be placed (in $cm$) so that its real image of size three times that of the object is obtained?

In an experiment to determine the focal length $(f)$ of a concave mirror by the $u-v$ method,a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with $PA$. When the student shifts his/her eye towards left,the image appears to the right of the object pin. Then,