The approximate analytic formula is obtained which describes the
radiation intensity in the Tamm problem (charge motion on a finite
interval) on finite distances. For the typical experimental situation, the
angular spectrum of the Cherenkov radiation broadens enormously and
differs essentially from that predicted by the Tamm formula. In addition,
the approximate analytic formula is found which takes into account both
the deceleration of a charge due to the energy losses and a finite
distance of the observation point. Both these effects contribute to the
broadening of the angular spectrum. The approximate analytic formulae are
in close agreement with the exact numerical calculations for the real
experimental situation. These formulae are applied to the description of
Cherenkov radiation produced by relativistic heavy ions in the Darmstadt
experiments. An experiment is proposed to check the broadening of the
Cherenkov angular spectrum arising from its measurement on finite
distances.