An object is placed in front of a concave mirror of focal length $f$. $A$ virtual image is formed with a magnification of $2$. To obtain a real image of the same magnification,the object has to be moved by a distance of:

In the parallax method for the determination of the focal length of a concave mirror, the object should always be placed:

$A$ square wire frame of side $3 \, cm$ is placed at a distance of $25 \, cm$ from a concave mirror of focal length $10 \, cm$. The area of the image is ........ $cm^2$.

$A$ student performed the experiment of determination of focal length of a concave mirror by $u-v$ method using an optical bench of length $1.5 \ m$. The focal length of the mirror used is $24 \ cm$. The maximum error in the location of the image can be $0.2 \ cm$. The $5$ sets of $(u, v)$ values recorded by the student (in $cm$) are: $(42, 56), (48, 48), (60, 40), (66, 33), (78, 39)$. The data set$(s)$ that cannot come from the experiment and is (are) incorrectly recorded,is (are):
$(A) (42, 56)$
$(B) (48, 48)$
$(C) (66, 33)$
$(D) (78, 39)$

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

An object $5 \ cm$ tall is placed $1 \ m$ from a concave spherical mirror which has a radius of curvature of $20 \ cm$. The size of the image is $...... \ cm$.