  The Kirchhoff law of thermal radiation, relating emissivity {\epsilon} and
absorptance {\alpha}, has been originally formulated for opaque bodies in
thermodynamic equilibrium with the environment. However, in many systems of
practical importance, both assumptions are often not satisfied. In this work,
we revisit the century-old law and examine the limits of its applicability in
an example of Er:YAG and Er:YLF dielectric crystals, potential radiation
converters for thermophotovoltaic applications. In our experiments, the (80
at.%) Er:YAG crystal was opaque between 1.45 {\mu}m and 1.64 {\mu}m. In this
spectral range, its absorptance {\alpha}({\lambda}) is spectrally flat and
differentiates from unity only by a small amount of reflection. The shape of
the emissivity spectrum {\epsilon}({\lambda}) closely matches that of
absorptance {\alpha}({\lambda}), suggesting that the Kirchhoff law can
adequately describe thermal radiation of opaque bodies, even if the requirement
of thermodynamic equilibrium is not satisfied. The(20 at.%) Er:YLF crystal had
smaller size, lower concentration of Er ions, and it was not opaque.
Nevertheless, its spectrum of emissivity {\epsilon}({\lambda}) had almost the
same shape (between 1.45 {\mu}m and 1.62 {\mu}m) as the spectrum of absorptance
{\alpha}({\lambda}) derived from the transmission measurements. This
observation is in line with our prediction that the spectra of emissivity and
absorptance should have identical shapes in optically thin slabs. We, thus,
show that the Kirchhoff law of thermal radiation can be extended (with caution)
even to not-opaque bodies away from the thermodynamic equilibrium.
