$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. Where will the image be formed?

An object of height $5 \, cm$ is placed at a distance of $1 \, m$ from a concave mirror of radius of curvature $20 \, cm$. What will be the height of the image in $cm$?

$STATEMENT-1$: 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.

$A$ concave mirror of radius of curvature $R$ has a circular outline of radius $r$. $A$ circular disc is to be placed normal to the axis at the focus,so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For $r \ll R$,the area of this disc has to be at least

The focal length of a concave mirror is $50 \, cm$. Where should an object be placed so that its image is two times magnified and inverted?

The focal length of a concave mirror is $f$ and the distance from the object to the principal focus is $x$. The magnification will be: