  A special case of the relativistic Doppler effect, which occurs when light
reflects from a moving mirror, is discussed. The classic formula for the
Doppler shift is derived in a fully non-relativistic fashion using basic facts
from geometry. The derivation does not involve Lorentz transformations, length
contractions and time dilations, and therefore is conceptually simpler than the
standard derivations in physics textbooks. This discussion can be useful for
teaching introductory physics and also for understanding the foundations of
special relativity.
