  Infrared interferometry of supergiant and Mira stars has recently been
reinterpreted as revealing the presence of deep molecular layers. Empirical
models for a photosphere surrounded by a simple molecular layer or envelope
have led to a consistent interpretation of previously inconsistent data. The
stellar photospheres are found to be smaller than previously understood, and
the molecular layer is much higher and denser than predicted by hydrostatic
equilibrium. However, the analysis was based on spatial observations with
medium-band optical filters, which mixed the visibilities of different spatial
structures. This paper reports spatial interferometry with narrow spectral
bands, isolating near-continuum and strong molecular features, obtained for the
supergiant mu Cep. The measurements confirm strong variation of apparent
diameter across the K-band. A layer model shows that a stellar photosphere of
angular diameter 14.11+/-0.60 mas is surrounded by a molecular layer of
diameter 18.56+/-0.26 mas, with an optical thickness varying from nearly zero
at 2.15 microns to >1 at 2.39 microns. Although mu Cep and alpha Ori have a
similar spectral type, interferometry shows that they differ in their radiative
properties. Comparison with previous broad-band measurements shows the
importance of narrow spectral bands. The molecular layer or envelope appears to
be a common feature of cool supergiants.
