In an optical bench experiment to determine the focal length of the concave mirror, the least count of the bench scale (meter scale) is $0.1\mathrm{cm}$. The object needle reading is $10.7\mathrm{cm}$ and the image needle reading is $5.7\mathrm{cm}$. The mirror is positioned at $15.7\mathrm{cm}$.

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_1$ from $C$ and the distance of the image formed is $d_2$ from $C,$ the radius of curvature of this mirror is:

An object of height $2.0 \mathrm{cm}$ is placed on the principal axis of a concave mirror at a distance of $12 \mathrm{cm}$ from the pole. If the image is inverted, real and $5 \mathrm{cm}$ in height then location of the image and focal length of the mirror respectively are

A point object is moving uniformly towards the pole of a concave mirror of focal length $25 \mathrm{cm}$ along its axis as shown below. The speed of the object is $1 {\mathrm{ms}}^{-1}$. At $t=0$, the distance of the object from the mirror is $50 \mathrm{cm}$. The average velocity of the image formed by the mirror between time $t=0$ and $t=0.25 \mathrm{s}$ is:

An object is placed at $10 \mathrm{cm}$ distance infront of a concave mirror of radius of curvature $40 \mathrm{cm}$. Find the position, nature and magnification of the image.