We present far-ultraviolet spectroscopy of the emission/reflection nebula IC 405 obtained by a rocket-borne long-slit spectrograph and the Far Ultraviolet Spectroscopic Explorer. Both data sets show a rise in the ratio of the nebular surface brightness to stellar flux (S/F_*) of approximately two orders of magnitude towards the blue end of the far-UV bandpass. Scattering models using simple dust geometries fail to reproduce the observed S/F_* for realistic grain properties. The high spectral resolution of the FUSE data reveals a rich fluorescent molecular hydrogen spectrum ~1000 north of the star that is clearly distinguished from the steady blue continuum. The S/F_* remains roughly constant at all nebular pointings, showing that fluorescent molecular hydrogen is not the dominant cause for the blue rise. We discuss three possible mechanisms for the ``Blue Dust: differential extinction of the dominant star (HD 34078), unusual dust grain properties, and emission from nebular dust. We conclude that uncertainties in the nebular geometry and the degree of dust clumping are most likely responsible for the blue rise. As an interesting consequence of this result, we consider how IC 405 would appear in a spatially unresolved observation. If IC 405 was observed with a spatial resolution of less than 0.4 pc, for example, an observer would infer a far-UV flux that was 2.5 times the true value, giving the appearance of a stellar continuum that was less extinguished than radiation from the surrounding nebula, an effect that is reminiscent of the observed ultraviolet properties of starburst galaxies.
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