The image formed by a convex mirror is always:

Assertion $(A):$ The relation among $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason $(R):$ The laws of reflection are strictly valid for plane surfaces but not for large spherical surfaces.

$A$ spherical mirror forms an erect image of an object,three times the size of the object. If the distance between the object and the image is $80 \ cm$,then the focal length of the mirror is ......... $cm$.

An object of height $5 \, cm$ is placed at a distance of $1 \, m$ from a concave mirror having a radius of curvature of $20 \, cm$. The height of the image is ....... $cm$.

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification $(m)$ versus distance of the object from the mirror $(x)$ is correctly given by
(Graphs are drawn schematically and are not to scale)

Derive the relationship between the focal length $(f)$ and the radius of curvature $(R)$ for a spherical mirror.