  The purpose of this paper is to investigate the spectral nature of the
Neumann-Poincar\'e operator on the intersecting disks, which is a domain with
the Lipschitz boundary. The complete spectral resolution of the operator is
derived, which shows in particular that it admits only the absolutely
continuous spectrum, no singularly continuous spectrum and no pure point
spectrum. We then quantitatively analyze using the spectral resolution the
plasmon resonance at the absolutely continuous spectrum.
