The list contains two contradictory pairs, so the work is to pick the right member of each: lossless rather than lossy, homogeneous rather than non-homogeneous, together with isotropic. That is (A), (C) and (E) — option 1.

(A) — lossless is what "perfect" means. A perfect dielectric has zero conductivity, so no conduction current flows and no energy is dissipated:

\(\sigma=0\quad\Rightarrow\quad\alpha=0\)

The attenuation constant vanishes and a wave propagates without decay. The loss tangent \(\tan\delta=\sigma/\omega\varepsilon\) is zero, and the propagation constant is purely imaginary:

\(\gamma=j\beta=j\omega\sqrt{\mu\varepsilon}\)

(C) — isotropic means the properties do not depend on direction. \(\varepsilon\) and \(\mu\) are scalars rather than tensors, so \(\vec{D}\) is parallel to \(\vec{E}\) and the wave travels at the same speed however it is oriented. Without this, a wave would split into two components with different velocities — birefringence, as in a crystal or a magnetised ferrite.

(E) — homogeneous means the properties do not depend on position. \(\varepsilon\) and \(\mu\) are the same everywhere, so there are no internal boundaries to reflect or refract the wave. This is what allows a single uniform plane-wave solution to hold throughout the medium.

The distinction between isotropic and homogeneous is the one most often blurred, and the table makes it precise: one is about direction, the other about place. A medium can be either without the other — a stack of uniform layers is isotropic but not homogeneous, and a uniformly magnetised ferrite is homogeneous but not isotropic.

What follows for the wave. Under all three conditions the intrinsic impedance is real,

\(\eta=\sqrt{\dfrac{\mu}{\varepsilon}}\)

so E and H are exactly in phase and the wave carries real power with no reactive component — the simple uniform plane wave of the textbooks.

Hence, the conditions are (A), (C) and (E).