Sorry for the butchered message. Here is the same message
again.
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.