  We performed optical spectroscopy measurement on a superconducting
Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ single crystal with T$_c$=37 K. Formation of
the superconducting energy gaps in the far-infared reflectance spectra below
T$_c$ is clearly observed. The gap amplitudes match well with the two distinct
superconducting gaps observed in angle-resolved photoemission spectroscopy
experiments on different Fermi surfaces. We determined absolute value of the
penetration depth at 10 K as $\lambda\simeq2000 \AA$. A spectral weight
analysis shows that the Ferrell-Glover-Timkham sum rule is satisfied at low
energy scale, less than 6$\Delta$.
