An image formed by a concave mirror of focal length $6 \, cm$ is $3$ times the size of the object. The distance of the object from the mirror is......$cm$.

An object is placed at $10 \text{ cm}$ in front of a concave mirror of focal length $15 \text{ cm}$. The image formed will be . . . . . . .

The graph between $u$ and $v$ for a convex mirror is

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

Two objects $A$ and $B$ are placed at $15\,cm$ and $25\,cm$ from the pole in front of a concave mirror having a radius of curvature $40\,cm$. The distance between the images formed by the mirror is $..........\,cm$.

Consider a light source placed at a distance of $1.5 \ m$ along the axis facing the convex side of a spherical mirror of radius of curvature $1 \ m$. The position $(s^{\prime})$,nature and magnification $(m)$ of the image are