  Localization of electrons in 1D disordered systems is usually described in
the random phase approximation, when distributions of phases \varphi and
\theta, entering the transfer matrix, are considered as uniform. In the general
case, the random phase approximation is violated, and the evolution equations
are written in terms of the Landauer resistance \rho and the combined phases
\psi=\theta-\varphi and \chi=\theta+\varphi. The distribution of the phase \psi
is found to exhibit an unusual phase transition at the point E_0 when changing
the electron energy E, which manifests itself in the appearance of the
imaginary part of \psi. The distribution of resistance P(\rho) has no
singularity at the point E_0, and the transition seems unobservable in the
framework of condensed matter physics. However, the theory of 1D localization
is immediately applicable to the scattering of waves propagating in a
single-mode optical waveguide. Modern optical methods open a way to measure
phases \psi and \chi. As a result, the indicated phase transition becomes
observable.
