Transverse displacement ol a totally reflected light beam and phase-shift method

We show that the transverse displacement of a totally reflected light beam calculated by the phase-shift method is the projection of the longitudinal displacement on the right section of Imbert's prism; and that the phase of the reflected beam has no derivative when the incident angle is the critical angle of total reflection. Based on Ashby and Miller's (1973) work we get general expression for this displacement. We obtain non-linear terms in m (number of reflections) when the beam takes a helical path in Imbert's total reflection prism. And we discuss the conditions requiered to find Ashby and Miller's and Julia and Neveu's (1973) expressions. When the light beam remains in the right section of Imbert's isosceles prism the phase-shift calculated transverse displacement is zero whereas the energy flux conservation method and Imbert's (1970) and Levy's (1973) experiments give non-zero results.