  Planetary nebulae (PNe) are expected to have a ~10$^{5}$ K interface layer
between the $\geq$10$^{6}$ K inner hot bubble and the ~10$^{4}$ K optical
nebular shell. The PN structure and evolution, and the X-ray emission depend
critically on the efficiency of mixing of material at this interface layer.
However, neither its location nor its spatial extent has ever been determined
so far. Using high-spatial resolution HST STIS spectroscopic observations of
the N V 1239,1243 lines in the Cat's Eye Nebula (NGC 6543), we have detected
this interface layer and determined its location, extent, and physical
properties for the first time in a PN. We confirm that this interface layer, as
revealed by the spatial distribution of the N V 1239 line emission, is located
between the hot bubble and the optical nebular shell. We estimate a thickness
of 1.5$\times$10$^{16}$ cm and an electron density of ~200 cm$^{-3}$ for the
mixing layer. With a thermal pressure of ~2$\times$10$^{-8}$ dyn cm$^{-2}$, the
mixing layer is in pressure equilibrium with the hot bubble and ionized nebular
rim of NGC 6543.
