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.
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