  We measured the in-plane optical conductivity of a nearly optimally doped
(Ba,K)Fe2As2 single crystal with Tc = 39.1 K. Upon entering the superconducting
state the optical conductivity below ~20 meV vanishes, strongly suggesting a
fully gapped system. A BCS-like fit requires two different isotropic gaps to
describe the optical response of this material. The temperature dependence of
the gaps and the penetration depth suggest a strong interband coupling, but no
impurity scattering induced pair breaking is present. This contrasts to the
large residual conductivity observed in optimally doped Ba(Fe,Co)2As2 and
strongly supports an s(+/-) gap symmetry for these compounds.
