10. Two plane mirrors are placed intersecting at an angle of $30^{\circ}$, with the intersection point at $V$. A horizontal beam of light is emitted from a source $S$, parallel to one of the mirrors $V W$, and reflects at point $A$ on the other mirror $U V$, then reflects again at point $B$ on mirror $V W$, and then reflects again at point $C$ on mirror $U V$. After several reflections, the light beam returns to $S$. If $S A=A V=1$, then the total distance traveled by the light beam is
$10.2+\sqrt{3}$.
As shown in Figure 11, because $S A / / W V$, combined with the optical principle that the angle of reflection equals the angle of incidence, the sizes of the angles are marked in the figure.

Because $\angle B C V=90^{\circ}$, the light beam will return along the original path to point $S$, so, the total path length of the light beam is
$$
\begin{array}{l}
2(S A+A B+B C) \\
=2\left(1+\frac{1}{\sqrt{3}}+\frac{1}{2 \sqrt{3}}\right)=2+\frac{3}{\sqrt{3}}=2+\sqrt{3} .
\end{array}
$$