An object is placed in front of a concave mirror of focal length $15 \ cm$. The image formed is twice the size of the object. If the image is virtual,the position of the object is at ...... $cm$.

An object is placed at a distance of $20 \ cm$ from the pole of a concave mirror of focal length $10 \ cm$. The distance of the image formed is

The convergence of a concave mirror can be decreased by dipping it in which of the following?

The shape of the image formed of an object $AB$ due to the concave mirror shown in the figure is best represented by (assume point $A$ is at the centre of curvature of the mirror):-

$A$ 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):
$(A) (42, 56)$
$(B) (48, 48)$
$(C) (66, 33)$
$(D) (78, 39)$

$A$ candle flame of $3\, cm$ is placed at $3\, m$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9\, cm$. Then $x$ is......$cm$.