  The fundamental dispersion relation of transverse electro-magnetic waves in a
cold collisionless plasma is formally equivalent to the two dimensional
dispersion relation of inertio-gravity waves in a rotating shallow water
system, where the Coriolis frequency can be identified with the plasma
frequency, and the shallow water gravity wave phase speed plays the role of the
speed of light. Here we examine this formal equivalence in the governing
linearised equations, and compare between the propagation wave mechanisms in
these seemingly unrelated physical systems.
