The shape of the image formed of an object $AB$ due to the concave mirror shown in the figure is best represented by (assume point $A$ is at the centre of curvature of the 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 rod of $5 \, cm$ length is kept along the axis of a concave mirror of $10 \, cm$ focal length such that its image is real and magnified. If one end of the rod is at a distance of $2f$ from the mirror,what will be its magnification?

$A$ candle flame of $3\, cm$ is placed at $3\, m$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9\, cm$. Then $x$ is......$cm$.

In the figure shown,the image of a real object $O$ is formed at point $I$. $AB$ is the principal axis of the mirror. The mirror must be:

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