$A$ boy stands $30 \,cm$ in front of a mirror. The height of his erect image is $1/5 \,th$ of his actual height. The mirror used is ..... .

An object is placed at a distance of $10 \, cm$ from a concave mirror of focal length $20 \, cm$. The image formed will be .......

Suppose while sitting in a parked car,you notice a jogger approaching towards you in the side view mirror of radius of curvature $R = 2 \; m$. If the jogger is running at a speed of $5 \; m s^{-1}$,how fast does the image of the jogger appear to move when the jogger is $(a) \; 39 \; m$,$(b) \; 29 \; m$,$(c) \; 19 \; m$,and $(d) \; 9 \; m$ away?

Define the focal plane of a concave mirror.

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.

$A$ thin cylindrical rod of length $10\,cm$ is placed horizontally on the principal axis of a concave mirror of focal length $20\,cm$. The rod is placed in such a way that the midpoint of the rod is at $40\,cm$ from the pole of the mirror. The length of the image formed by the mirror will be $\frac{x}{3}\,cm$. The value of $x$ is $............$.