At what distance in front of a concave mirror of focal length $30\; cm$,should an object be placed (in $cm$) so that its real image of size three times that of the object is obtained?

An object of size $7.5 \ cm$ is placed in front of a convex mirror of radius of curvature $25 \ cm$ at a distance of $40 \ cm$. The size of the image should be ........ $cm$.

Define the following for curved mirrors: $(1)$ Radius of curvature,$(2)$ Centre of curvature,$(3)$ Pole,$(4)$ Principal axis,$(5)$ Aperture,$(6)$ Principal focus,$(7)$ Focal plane,$(8)$ Focal length,$(9)$ Paraxial rays.

An object is placed beyond the centre of curvature $C$ of a concave mirror. If the distance of the object is $d_{1}$ from $C$ and the distance of the image formed is $d_{2}$ from $C$,the radius of curvature of this mirror is

An object $5 \ cm$ tall is placed $1 \ m$ from a concave spherical mirror which has a radius of curvature of $20 \ cm$. The size of the image is $...... \ cm$.

$A$ straight line joining the object point and image point is always perpendicular to the mirror: