$A$ concave mirror of focal length $15\, cm$ forms an image having twice the linear dimensions of the object. The position of the object when the image is virtual will be........$cm$

$A$ concave mirror is used to focus the image of a flower on a nearby wall $120 \ cm$ from the flower. If a lateral magnification of $16$ is desired,the distance of the flower from the mirror should be $... \ cm$.

Draw the ray diagram when an object is placed between the focus $(F)$ and the pole $(P)$ of a concave mirror.

$A$ person wants a real image of his own,$3$ times enlarged. Where should he stand in front of a concave mirror of radius of curvature $30 \ cm$ (in $cm$)?

$A$ $2.0 \,cm$ object is placed $15 \,cm$ in front of a concave mirror of focal length $10 \,cm$. What is the size and nature of the image?

In an experiment to determine the focal length $(f)$ of a concave mirror by the $u-v$ method,a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with $PA$. When the student shifts his/her eye towards left,the image appears to the right of the object pin. Then,