  We give a complete description, provided with a mathematical proof, of the
shape of the spectrum of the Hill operator with a PT-symmetric periodic optical
potential. We prove that the second critical point, after which the real parts
of the first and second bands disappear, is a number between 0.8884370025 and
0.8884370117. Moreover we prove that it is the degeneration point for the first
periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary
precise value of the second critical point as well as the k-th critical points
after which the real parts of the (2k-3)th and (2k-2)th bands disappear, where
k=3,4,...
