This message has to do with an area of physics which is often skipped
in introductory courses. But those who teach optics should be able to
decide whether or not my claim about a contradiction is valid.
An optical axis of a transparent crystal, such as quartz, is a direction
along which ordinary and extraordinary waves propagate with the same
phase velocity. A typical illustration of this can be found in
"Fundamentals
of Optics" of Jenkins and White (Fig 26A, p 545, 4th edition).
Consider a quartz plate whose optical axes are also normal to its flat
surfaces. In such plate a linearly polarized light, at zero angle of
incidence, will remain linearly polarized at the exit, no matter how
thick
is the plate. We explain this by saying that the wave velocity, for that
direction of propagation, is the same for all planes of polarization.
The explanation makes sense but it conflicts with another so-called
explanation, at least in my mind. I am referring to Frenel's
"explanation"
of optical activity (rotation of the plane of polarization by a quartz
plate).
According to Jenkins and White (page 588) Frenel's explains the effect
by assuming that "two circular vibrations move forward with slightly
different velocities."
Please explain how velocities of right-handed and left-handed components
of linearly polarized light can be different for a beam parallel to the
optical
axes. Didn't we already say that for this particular direction the speed
of
light does not depend on the orientation of its plane of polarization? A
circularly polarized light is a superposition of two linearly polarized
lights (when amplitudes are equal, planes of polarization orthogonal and
phases shifted by 90 degrees).
If all four linearly polarized components (of circularly polarized
lights, left
and right) have the same speed then speeds of circularly polarized lights
must also be equal. They can not be slightly different, as postulated by
Fresnel. Do you agree that we are facing a contradiction? It is not only
Jenkins and White; many textbooks say the same thing. See Hecht and
Zajac, for example, where Fresnel's "explanation" is formally presented
in terms of unit vectors, i and j.
My point is not that Fresnel was wrong; he was only saying (in 1825) that
optical activity (discovered in quartz by Arago in 1811) would be
consistent
with the hypothesis of different phase velocities of left and right
light. That
is true, mathematically. But as far as physics is concerned this
hypothesis is
in conflict with what we know about linearly polarizied beams traveling
along optical axes. Perhaps I missing something significant. What is it?
Once again, I am not looking for an explanation of optical activity
(which
is probably due to helical arrangements of "electron clouds"); I am
trying
to expose an apparent contradiction of what is stated in many textbooks.
Ludwik Kowalski
Department of Mathematical Sciences
Montclair State University, New Jersey.