  In this paper, we investigate statistics on alternating words under
correspondence between ``possible reflection paths within several layers of
glass'' and ``alternating words''. For
$v=(v_1,v_2,\cdots,v_n)\in\mathbb{Z}^{n}$, we say $P$ is a path within $n$
glass plates corresponding to $v$, if $P$ has exactly $v_i$ reflections
occurring at the $i^{\rm{th}}$ plate for all $i\in\{1,2,\cdots,n\}$. We give a
recursion for the number of paths corresponding to $v$ satisfying $v \in
\mathbb{Z}^n$ and $\sum_{i\geq 1} v_i=m$. Also, we establish recursions for
statistics around the number of paths corresponding to a given vector
$v\in\mathbb{Z}^n$ and a closed form for $n=3$. Finally, we give a equivalent
condition for the existence of path corresponding to a given vector $v$.
