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Re: [Phys-L] Snell +- history +- logic



On 04/11/2014 02:47 PM, Bob Sciamanda wrote:
Snell's law is a special case of Huygen's principle, applied to a
plane wave travelling from one homogeneous medium into a second
homogeneous medium, with a clearly defined discontinuity at the
interface. For a continuously (spatially) varying index of
refraction, the wavefront (not a "ray") must be followed using
Huygen's principle.

There are at least four ways of agreeing or disagreeing
with that statement, depending on whether we wish to
emphasize physics, pedagogy, logic, or history.

As a point of physics, as we understand it today, light
(and everything else) is a wave. Rays, to the extent
they exist at all, exist only as a special case, a
limiting case. This can be formalized using the
method of stationary phase.

As a point of pedagogy, that's how things should be
presented to students.

However, as a point of logic, it is certainly possible
to conceive of a world where raylike rays of light are
primary and fundamental.

As a point of history, that's exactly what happened.
Snell's law was invented and re-invented several times,
long before there was any connection to waves. In
particular, one can postulate Fermat's principle of
least time as a first principle. One can apply it
on a ray-by-ray basis, as a way of deriving and/or
explaining Snell's law ... without mentioning waves.

====

If you look elsewhere, you can find plenty of evidence
for waves, e.g. lasers, diffraction gratings, Newton's
rings, et cetera ... but logically speaking, Snell's
law does not require waves.

This brings us to a point I've mentioned eleventeen times
before: Students -- especially in the introductory course --
should be given the best evidence and the best explanations,
not the most ancient evidence or the most ancient explanations.

A lot of people -- including some on this list -- claim
to use the "historical approach" as a means of organizing
and motivating the physics course. I simply do not
believe these claims. I cannot imagine anybody sadistic
enough to retrace the historical development of Snell's
law in the introductory course.

If somebody wants to liven up the course with some anecdotes
about the olden days, I suppose that's OK, within limits
... but as the saying goes, the plural of "anecdote" is
not "data", and a succession of anecdotes is not history,
not even close. We should not pretend that it is.