  We show that a two-dimensional photonic crystal (PC) made from a non-magnetic
dielectric is a left-handed material in the sense defined by Veselago. Namely,
it has negative values of both the electric permittivity $\epsilon$ and the
magnetic permeability $\mu$ in some frequency range. This follows from a
recently proven general theorem. The negative values of $\epsilon$ and $\mu$
are found by a numerical simulation. Using these values we demonstrate the
Veselago lens, a unique optical device predicted by Veselago. An approximate
analytical theory is proposed to calculate the values of $\epsilon$ and $\mu$
from the PC band structure. It gives the results that are close to those
obtained by the numerical simulation. The theory explains how a non-zero
magnetization arises in a non-magnetic PC.
