$A$ concave shaving mirror has a radius of curvature of $35.0 \, cm$. It is positioned so that the upright image of a man's face is $2.5 \, times$ the size of the face. How far is the mirror from the face in $cm$?

$A$ short straight object of length $l$ lies along the central axis of a spherical concave mirror,at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$,then the ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume $l << X$ and $l << F$):

Assertion : The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason : Laws of reflection are strictly valid for plane surfaces,but not for large spherical surfaces.

All of the following statements are correct except:

Define the focal plane of a concave mirror.

The figure shows a small concave mirror with $CP$ as its principal axis. $A$ ray $XY$ is incident on the mirror. Which of the four rays can be the reflected ray?