A new derivation of the relativistic aberration formula for a plane-polarized
light wave is presented that does not require any use of the Lorentz
transformation. The method is based on a modification of the Huygens-Fresnel
principle to include the relativistic effects introduced by the relative motion
between the observer and the emitter. The derivation clearly shows that the
aberration formula is a direct consequence of the relative simultaneity.
The formula for the frequency shift of a plane-polarized light wave reflected
from a uniformly moving mirror is derived directly from the constant light
speed postulate and the basic principles of wave optics. Unlike the original
derivation by Einstein, our derivation does not involve Lorentz
transformations. As such, it lies within the scope of a first course in special
relativity.
