$A$ virtual image three times the size of the object is obtained with a concave mirror of radius of curvature $36 \ cm$. The distance of the object from the mirror is ........ $cm$.

$A$ mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between the object and its image is $40 \ cm$,then the focal length of the mirror is . . . . . . . (in $cm$)

$A$ thin rod of $5 \, cm$ length is kept along the axis of a concave mirror of $10 \, cm$ focal length such that its image is real and magnified. If one end of the rod is at a distance of $2f$ from the mirror,what will be its magnification?

The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image:

$A$ convergent beam of light is incident on a convex mirror so as to converge to a distance $12 \, cm$ from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror? $(cm)$

$A$ candle of height $3 \ cm$ is placed at $300 \ cm$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9 \ cm$. Then $x$ is $.... \ cm$.