The minimum distance between the object and its real image for a concave mirror is

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?

$A$ short straight object of height $100\, cm$ lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40\, cm$. The image of the object produced by the mirror is of height $25\, cm$ and has the same orientation as the object. One may conclude from the information:

The distance of a real object from the focus of a convex mirror of radius of curvature $a$ is $b$. Then the distance of the image from the focus is

$A$ ray of light is incident on a convex mirror along a vector $3\hat i + 4\hat j + 12\hat k$. The normal to the convex mirror at the point of incidence is along $3\hat i + 4\hat j$. The unit vector along the reflected ray is:

If the lateral magnification is $-2$ for a virtual object in a spherical mirror,then: