In this work we present measurements of the anisotropic optical respon
se of YBa2Cu4O8. By using ellipsometry and reflectance measurements, w
e obtained all three components of the dielectric tensor in the energy
range between 0.05 and 5.5 eV. We report the existence of a plasma ed
ge for light polarized perpendicular to the CuO2 planes. For the in-pl
ane optical response, Drude-Lorentz fits to our reflectance spectra sh
ow a behavior that differs qualitatively from that reported for YBa2Cu
3O7, namely that the scattering frequency for the carriers in the chai
n is smaller than for the plane carriers. We assign this to the stabil
ity of the chains against oxygen loss and disorder. We have isolated t
he contribution of interband transitions to the dielectric function an
d compare it to results from an ab initio calculation. For the computa
tion of the one-electron states we used the linear-muffin-tin-orbital
method in the atomic-sphere approximation. We find good agreement betw
een the calculated and the measured spectra, hinting at the validity o
f the underlying one-electron local-density approximation. We give a m
icroscopic explanation of the observed structure in the optical respon
se and point out the main differences between the band structures of Y
Ba2Cu4O8 and YBa2Cu3O7 as they manifest themselves in the optical prop
erties.