$A$ thin rod of $5 \, cm$ length is kept along the axis of a concave mirror of $10 \, cm$ focal length such that its image is real and magnified. If one end of the rod is at a distance of $2f$ from the mirror,what will be its magnification?

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,

An object is placed $40\;cm$ from a concave mirror of focal length $20\;cm.$ The image formed is

An object placed in front of a concave mirror of focal length $0.15 \,m$ produces a virtual image,which is twice the size of the object. The position of the object with respect to the mirror is ........... $cm$. (in $.5$)

$A$ square of side $3 \ cm$ is placed at a distance of $25 \ cm$ from a concave mirror of focal length $10 \ cm$. The center of the square is on the axis of the mirror and the plane is perpendicular to the axis. The area enclosed by the image of the square is ........ $cm^2$.

An object is placed at a distance of $40 \, cm$ from a concave mirror of focal length $15 \, cm$. If the object is displaced through a distance of $20 \, cm$ towards the mirror,the displacement of the image will be: