The image formed by a concave mirror is real and of the same size. Where is the object placed?

$A$ $4.5\, cm$ needle is placed $12\, cm$ away from a convex mirror of focal length $15\, cm$. Give the location of the image and its magnification.

State the sign convention used to measure the length of the image and the object.

$(a)$ Define principal focus of a spherical mirror.
$(b)$ For what position of the object does a concave mirror form a real,inverted and diminished image of the object? Draw the ray diagram.
$(c)$ An object $4 \,cm$ high is placed at a distance of $6 \,cm$ in front of a concave mirror of focal length $12 \,cm$. Find the position of the image formed.

An object is placed at a distance of $12 \ cm$ in front of a concave mirror. It forms a real image four times larger than the object. Calculate the distance of the image from the mirror. (in $cm$)

The distance between the object kept at $2 \, m$ from a plane mirror and its image is $.....$ (in $, m$)