  In this paper a wave is generated by an initial data whose support is
localized at the outside of unknown obstacles and observed in a limited time on
a known closed surface or the same position as the support of the initial data.
The observed data in the latter process are nothing but the back-scattering
data. Two types of obstacles are considered. One is obstacles with a
dissipative boundary condition which is a generalization of the sound-hard
obstacles; another is obstacles with a finite refractive index, so-called,
transparent obstacles. For each type of obstacles two formulae which yield
explicitly the distance from the support of the initial data to unknown
obstacles are given.
