Re: REFRACTION - REFLECTION

[Leigh Palmer <palmer@sfu.ca>]

Herb said:

> > Herb Gottlieb from New York City
> > (Where wavefronts have learned that they must ALWAYS be
> > perpendicular to the direction of wave propagation)

I said:

> > Better slack off on that a bit, Herb. It is only a requirement
> > for waves with lightspeed group velocities. In birefringent
> > materials (calcite, for example) the wavefronts need not be
> > perpendicular to their directions of propagation.

David Bowman said:

> Sorry to disagree with you here, Leigh, but the group velocities are
> not relevant.  The entire dispersion relation [omega](k) is irrelevant
> for monochromatic waves.  Refraction (and total internal reflection, etc.)
> happens *separately* for each of the superposed monochromatic waves.  If
> the media is/are dispersive, then the rays of the various frequencies may
> follow different paths (such as through a prism) because the phase velocity
> may be frequency dependent, however.  Birefringence is a complication which
> only can occur for waves whose wave function is tranverse-vector-valued
> (e.g. EM waves) where one transverse polarization has a different
> dispersion relation function [omega](k) than the other orthogonal one.
> Refraction effects can occur for waves which are not vector-valued.
> Refraction can occur (and also wave motion remains perpendicular to the
> wavefronts) for scalar-valued waves, longitudinal waves, spinor waves and
> tensor waves as well.  The very concept of polarization doesn't even make
> sense for a scalar or a longitudinal wave.  There is no such thing as
> birefringence for acoustic waves propagating through the interface of two
> immisible fluids (of differing density and/or bulk modulus), but there
> *are* refraction effects as well as wave motions perpendicular to the
> local wavefronts. In short, refraction effects and the perpendicularity of
> the wave fronts to the wave's motion depend on the *argument* of the
> running wave function, but polarization effects depend on the *value* space
> of that function.

I think I must stick by my original statement. Herb did not refer
to light waves. He said, simply, "waves" and used the dangerous
term "ALWAYS". I believe my statement is entirely correct.

When transverse waves propagate in an anisotropic medium, even
light waves, the propagation direction need not be perpendicular
to the wavefront. Consider the simple case of double refraction
of an unpolarized light wave normally incident on calcite. One
polarized component of the wave (the "ordinary ray") propagates
into the crystal in the initial direction and its wavefronts, or
surfaces of constant phase, are perpendicular to that direction.
The other component (the "extraordinary ray") propagates in a
different direction, but its surfaces of constant phase are
constrained by symmetry to be parallel to those of the incident
wave in order to match at the interface. Thus the wavefronts are
not perpendicular to the direction of propagation, as I said.

Leigh