An object of length $6 \ cm$ is placed on the principal axis of a concave mirror of focal length $f$ at a distance of $4f$. The length of the image will be......$cm$.

$A$ 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 $cm$)

$A$ convex lens (of focal length $20\, cm$) and a concave mirror,having their principal axes along the same lines,are kept $80\, cm$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30\, cm$ to the left of the convex lens,its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror,by itself,would produce a virtual image would be.....$cm$.

$A$ beam of light is converging towards a point $O$ behind a convex mirror of focal length $20 \, cm$. If the point $O$ is $10 \, cm$ behind the mirror,then the position of the image is at a distance of ..... $cm$.

$A$ 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 $.0$)

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