The focal length of a concave mirror is $50 \, cm$. Where should an object be placed so that its image is two times magnified and inverted?

$A$ 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.....$cm$.

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

Distance between an object and its three times magnified real image is $40 \ cm$. The focal length of the mirror used is . . . . . . $cm$.

Which of the following graphs represents the magnification of a real image against the distance from the focus of a concave mirror?

The primary purpose of using a parabolic mirror in a reflecting telescope is