$A$ small rod of length $2 \, mm$ lies along the principal axis at a distance of $30 \, cm$ from a concave mirror of focal length $20 \, cm$. The axial length of the image of the rod is.....$mm$.

$A$ straight metal rod of length $6 \ cm$ is placed along the principal axis of a concave mirror of focal length $9 \ cm$ such that the end of the rod closer to the mirror is at a distance of $15 \ cm$ from the pole of the mirror. The length of the image of the rod is (in $cm$)

An object of height $5 \, cm$ is placed at a distance of $1 \, m$ from a concave mirror having a radius of curvature of $20 \, cm$. The height of the image is ....... $cm$.

Use the mirror equation to deduce that:
$(a)$ an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.
$(b)$ a convex mirror always produces a virtual image independent of the location of the object.
$(c)$ the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
$(d)$ an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

Draw the ray diagram when an object is placed between the focus $(F)$ and the pole $(P)$ of a concave mirror.

An object is placed at a distance of $18 \ cm$ in front of a mirror. If the image is formed at a distance of $4 \ cm$ on the other side,then the focal length,nature of the mirror,and nature of the image are respectively: