  We compare shadows cast by Schwarzschild black holes with those produced by
two classes of naked singularities that result from gravitational collapse of
spherically symmetric matter. The latter models consist of an interior naked
singularity spacetime restricted to radii $r\leq R_b$, matched to Schwarzschild
spacetime outside the boundary radius $R_b$. While a black hole always has a
photon sphere and always casts a shadow, we find that the naked singularity
models have photon spheres only if a certain parameter $M_0$ that characterizes
these models satisfies $M_0\geq 2/3$, or equivalently, if $R_b\leq 3M$, where
$M$ is the total mass of the object. Such models do produce shadows. However,
models with $M_0<2/3$ (or $R_b>3M$) have no photon sphere and do not produce a
shadow. Instead, they produce an interesting `full-moon' image. These results
imply that the presence of a shadow does not by itself prove that a compact
object is necessarily a black hole. The object could be a naked singularity
with $M_0\geq 2/3$, and we will need other observational clues to distinguish
the two possibilities. On the other hand, the presence of a full-moon image
would certainly rule out a black hole and might suggest a naked singularity
with $M_0<2/3$. It would be worthwhile to generalize the present study, which
is restricted to spherically symmetric models, to rotating black holes and
naked singularities.
