The focal length of a concave mirror is $50 \ cm$. At what distance (in $cm$) should an object be placed to obtain a real and inverted image of double the size?

An object is placed in front of a spherical mirror, and a $2$ times magnified image is formed on a screen. Choose the $\text{CORRECT}$ option.

Write the mirror equation for a spherical 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):
$(A) (42, 56)$
$(B) (48, 48)$
$(C) (66, 33)$
$(D) (78, 39)$

$A$ convex mirror of focal length $f$ is placed at the origin with its reflecting surface towards the negative $x-$ axis. Choose the correct graph between $v$ and $u$ for $u < 0$.

$A$ $4.5 \;cm$ needle is placed $12 \;cm$ away from a convex mirror of focal length $15 \;cm$. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.