The focal length of a concave mirror is $12\; cm$. Where should an object of length $4\; cm$ be placed,so that a real image of $1\; cm$ length is formed (in $; cm$)?

An object $2.5 \, cm$ high is placed at a distance of $10 \, cm$ from a concave mirror of radius of curvature $30 \, cm$. The size of the image is ........ $cm$.

$A$ ray of light is incident on a concave mirror. It is parallel to the principal axis and its height from the principal axis is equal to the focal length of the mirror. The ratio of the distance of point $B$ (where the reflected ray intersects the principal axis) to the distance of the focus from the centre of curvature is ($AB$ is the reflected ray).

An object is placed at a distance of $40 \ cm$ in front of a concave mirror of focal length $20 \ cm$. The image produced is

$A$ short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$, then the ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume $l << X$ and $l << F$):

$A$ convergent beam of light is incident on a convex mirror so as to converge to a distance $12 \, cm$ from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror? $(cm)$