A concave mirror is made by cutting a portion of a hollow glass sphere of radius 24 cm. Find the focal length of the mirror.

The distance between a mirror's pole and focus point called its focal length.
The focal point is where all parallel rays really or seemingly converge.
We already know that the focal length of a small-size spherical mirror is equal to half its radius of curvature.
So, we can write$f=R/2$
Where
$f$ = focal length
$R$ = Radius of sphere or sometimes known as radius of curvature

Think of a concave mirror like the one in figure
The second law of reflection, which states that the angle of reflection is always equal to the angle of incidence, states as such.
in order to write
$\mathrm{\angle }r=\mathrm{\angle }i$
Where,
$\mathrm{\angle }i=$ angle of incidence
$\mathrm{\angle }r=$angle of reflection
We are aware that AB is perpendicular to the main axis, $\mathrm{\angle }i$ and $\mathrm{\angle }\theta$ different angles. 

They must thus be equal.
$\because \angle i=\angle \theta ---\left(1\right)$

We are aware that a triangle has equal sides on either side of equal angles.
So, In $$\begin{gathered} △CFB △ C F B \\ FC=FB---\left(2\right) \end{gathered}$$
The mirror is quite close to the primary axis since we are aware that it is compact and focussed.
in order to write
$FB=FP---(3)$
Form (2) & (3) we get
$FC=FB=FP---\left(4\right)$
Figure demonstrates what
$CP=FC+FP---\left(5\right)$
Additional FC = FP switch from (4)
$$\begin{gathered} CP=FP+FP \\ CP=2FP \end{gathered}$$

We know $CP=R$ and $FP=f$
$$\begin{gathered} R=2ff=R/2 \\ So, f=R/2=24/2=12 cm \end{gathered}$$

Hence, the correct answer is option B.