I'm piggybacking on my wife's subscription (hope that's OK) and have a
question that may interest others as well.
I plan to give a short discovery-type lesson demonstrating: If a line
divides a plane so that a tourist travels at speed v in one half-plane and
speed w in the other half-plane, and if A and B are in different half-planes
then the fasted route from A to B is along a bent line obeying Snell's law.
I would like to be historically correct.
My encyclopedia tells me that Snell discovered/published his law of
refraction of light in 1621. This is usually stated v/w=sin theta/sin phi
where theta and phi are the path angles to the normal at the interface.
But of course the speeds v and w were totally unknown at the time, or so
I understand, so it seems unlikely the law was formulated in exactly that
way: sin theta/sin phi = const seems like a law that could be empirically
discovered/verified. The constant depending on the two media.
So Q1: What did Snell discover/assert?
Next, as I understand it, Fermat showed that Snell's result could be
derived by assuming light follows a minimum time path (local minimum
anyway) with light speed dependent upon medium. That is, he derived the
usual formulation.
Q2: Was there any consensus at the time that the speed of light was even
finite? Was this another brilliant insight of Fermat or had there been
some previous speculation along these lines? His proof, without calculus,
is brilliant mathematics but what was the status of physical thought at
the time?
Finally, Q3. This is probably an item where the record is easier to discover:
Who/when/how empirically worked out the speed of light in space/air/water/etc.?
References will suffice, I'll look it up.
I appreciate any helpful comments and I apologize if I have inadvertently
misused the list. In particular this is a "reply" since I don't see how to
just "start". Sorry.
Ken Berg
Dept. of Math.
Univ. of MD.