$A$ straight metal rod of length $6 \ cm$ is placed along the principal axis of a concave mirror of focal length $9 \ cm$ such that the end of the rod closer to the mirror is at a distance of $15 \ cm$ from the pole of the mirror. The length of the image of the rod is (in $cm$)

When an object is placed at a distance of $25 \ cm$ from a concave mirror,the magnification is $m_1$. The object is moved $15 \ cm$ farther away with respect to the earlier position and the magnification becomes $m_2$. If $m_1/m_2 = 4$,the focal length of the mirror is $....... \ cm$ (Assume image is real and $m_1, m_2$ are numerical values).

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.

$STATEMENT-1$: The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because
$STATEMENT-2$: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

An object is placed at the principal focus of a convex mirror. The image will be at

You are asked to design a shaving mirror assuming that a person keeps it $10\,cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25\,cm$. The radius of curvature of the mirror would then be.....$cm$.