  There are many two-by-two matrices in layer optics. It is shown that they can
be formulated in terms of a three-parameter group whose algebraic property is
the same as the group of Lorentz transformations in a space with two space-like
and one time-like dimensions, or the $Sp(2)$ group which is a standard
theoretical tool in optics. Among the interesting mathematical properties of
this group, the Iwasawa decomposition drastically simplifies the matrix algebra
under certain conditions, and leads to a concise expression for the S-matrix
for transmitted and reflected rays. It is shown that the Iwasawa effect can be
observed in multi-layer optics, and a sample calculation of the S-matrix is
given.
