Consider the following statements regarding an object placed between the pole and the focus of a concave mirror: $I$. The image is real. $II$. The image is magnified. $III$. The image is erect. Which of the following is correct?

The cross-section of a reflecting surface is represented by the equation $x^{2}+y^{2}=R^{2}$ as shown in the figure. $A$ ray travelling in the positive $x$ direction is directed toward the positive $y$ direction after reflection from the surface at point $M$. The coordinate of the point $M$ on the reflecting surface is

$A$ rod of length $10 \text{ cm}$ lies along the principal axis of a concave mirror of focal length $10 \text{ cm}$ as shown in the figure. The length of the image is . . . . . . $\text{cm}$.

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

How is it convenient to obtain an image by reflection from a spherical mirror?

What can be the largest distance of an image of a real object from a convex mirror of radius of curvature $10\,cm$?