  This submission presents the English translation of the early paper by
N.Kristoffel appeared in Russian in the Proceedings 0f the Tartu State
University No 42 p.94-112, 1956. It reflects the work done in Tartu State
University (Estonia)1n 1950-s on the total internal reflection and associated
effects. This paper can be of interest for the scientific community because it
remained not well known during the long period. The conceptual paper of
N.Kristoffel mentioned includes as the central result the prediction of the
transversal shift of the totally reflected light beam.
