  The possibility of making an optically large (many wavelengths in diameter)
object appear invisible has been a subject of many recent studies. Exact
invisibility scenarios for large (relative to the wavelength) objects involve
(meta)materials with superluminal phase velocity (refractive index less than
unity) and/or magnetic response. We introduce a new approximation applicable to
certain device geometries in the eikonal limit: piecewise-uniform scaling of
the refractive index. This transformation preserves the ray trajectories, but
leads to a uniform phase delay. We show how to take advantage of phase delays
to achieve a limited (directional and wavelength-dependent) form of
invisibility that does not require loss-ridden (meta)materials with
superluminal phase velocities.
