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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 superconductingstate the optical conductivity below ~20 meV vanishes, strongly suggesting afully gapped system. A BCS-like fit requires two different isotropic gaps todescribe the optical response of this material. The temperature dependence ofthe gaps and the penetration depth suggest a strong interband coupling, but noimpurity scattering induced pair breaking is present. This contrasts to thelarge residual conductivity observed in optimally doped Ba(Fe,Co)2As2 andstrongly supports an s(+/-) gap symmetry for these compounds.

Optical conductivity of Ba0.6 K0.4 Fe2 As2 : The effect of in-plane and out-of-plane doping in the superconducting gap