$A$ concave mirror has a focal length $20\,cm$. The distance between the two positions of the object for which the image size is double of the object size is......$cm$

An object is placed at $20 \ cm$ in front of a concave mirror,which produces a three times magnified real image. What is the focal length of the concave mirror (in $cm$)?

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 . . . . . $\text{cm s}^{-1}$.

An object of length $f/3$ is placed on the principal axis of a concave mirror of focal length $f$. The image of the end of the object farthest from the mirror is formed at the same position. Find the length of the image.

$A$ rod of length $10\, cm$ lies along the principal axis of a concave mirror of focal length $10\, cm$ in such a way that its end closer to the pole is $20\, cm$ away from the mirror. The length of the image is ......$cm$.

$A$ man having height $6 \ m$ observes an erect image of height $2 \ m$. The mirror used is: