  We theoretically investigate charge dynamics in weakly coupled $CuO_2$ planes
of the cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$ (CNCOC) using Kubo formula for
optical conductivity in the underdoped regime. The spectral function needed in
Kubo formula is obtained from an analytical form of electron Green's function
proposed (ansatz) by Yang-Rice-Zhang (YRZ) for the underdoped cuprates based on
their previous renormalized mean field theory and on the investigations of
weakly coupled Hubbard ladders. Although to an unaided eye the results of the
numerical calculation look very similar to that found experimentally in [K.
Waku etal. 2004] but a careful examination with extended Drude formalism shows
that YRZ ansatz for the calculation of optical conductivity is not sufficient
to understand the charge dynamics in $CuO_2$ planes of the cuprate CNCOC. More
physics is needed especially electromagnetic response from bound charges.
