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 ...... $cm$.

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

$A$ concave mirror of focal length $10 \, cm$ is immersed in water $(\mu = 4/3)$. The new focal length will be ...... $cm$.

An object of length $6 \ cm$ is placed at a distance of $4f$ on the principal axis of a concave mirror of focal length $f$. The length of the image will be ......$cm$.

The direction of a ray of light incident on a concave mirror is shown by $PQ$, where $PQ$ is parallel to the principal axis. The direction in which the ray would travel after reflection is shown by four rays marked as $A$, $B$, $C$ and $D$. Which of the four rays correctly shows the direction of the reflected ray?

An object is placed at a distance of $40 \ cm$ in front of a concave mirror of focal length $20 \ cm$. The image produced is