  Ultrathin Bi$_{2}$Te$_{3}$ single crystals laid on Scotch tape are
investigated by Fourier transform infrared spectroscopy at $4$K and in a
magnetic field up to $35$T. The magneto-transmittance spectra of the Bi$_{2}$%
Te$_{3}$/tape composite are analyzed as a two-layer system and the optical
conductivity of Bi$_{2}$Te$_{3}$ at different magnetic fields are extracted. We
find that magnetic field modifies the optical conductivity in the following
ways: (1) Field-induced transfer of the optical weight from the lower frequency
regime ($<250$cm$^{-1}$) to the higher frequency regime ($% >250$cm$^{-1}$) due
to the redistribution of charge carriers across the Fermi surface. (2) Evolving
of a Fano-resonance-like spectral feature from an anti-resonance to a resonance
with increasing magnetic field. Such behavior can be attributed to the
electron-phonon interactions between the $% E_{u}^{1}$ optical phonon mode and
the continuum of electronic transitions. (3) Cyclotron resonance resulting from
the inter-valence band Landau level transitions, which can be described by the
electrodynamics of massive Dirac holes.
