Re: glass ...

[Leigh Palmer <palmer@sfu.ca>]

John Mallinckrodt tantalized me with:

> On the other hand, if the prism is equilateral, you can take advantage of
> a very nice property of the internally reflected light to find the angle
> of minimum deviation quite accurately.  In this case collimated incident
> light of all wavelengths that suffers three (properly ordered) internal
> reflections with the prism sides will emerge once again collimated.
> Furthermore, the propagation direction is precisely that of noninternally
> reflected light of the particular wavelength which happens to be at its
> minimum deviation for the specific prism orientation. (Boy does the above
> ever need a figure!)

It took me more than an hour to derive this result. It turns out that
there is a more general version; what John says here is true for any
isosceles triangle if the second internal reflection is off the base
(the odd-length side). Since the law of reflection is symmetrical, it
is easily seen that both incident and reflected rays at the base must
make equal angles with respect to the other two faces, so symmetrical
passage* is guaranteed, independent of wavelength, for the thrice
internally reflected ray. Minimum deviation coincides in angles with
symmetrical passage, so the internally reflected ray satisfies that
condition too. We only have two-surface prisms in our labs, I suggest
that this is done to suppress the thrice reflected ray!.

Unfortunately I didn't see the simple derivation until after I had
solved the general scalene triangle case. It is quite tedious, and I
threw away several sheets of paper with algebraic errors on them.

I seem to have upset several people with my tirade against apostasy
regarding the status of entropy. Contrary to what I'm being told I
maintain that I did not call anyone stupid or accuse anyone of being
a postmodernist or a Creationist. I certainly did call one question
(roughly: Precisely how many degrees of freedom must a system possess
before thermodynamics applies to it?) stupid, and perhaps that implies
I felt the questioner was stupid. I ignored the question because I
felt it must have been, at best, a rhetorical device. I thought I had
assuaged the questioner (I complimented him later, and I even sent him
something of value) but he is still unhappy, and I can't apologize for
anything I say in which I believe. I did not intend my comments to be
hurtful, and I regret any hurt I may have caused, but I guess my skin
is thicker than others'.

Therefore I am sentencing myself to a month in the penalty box. This
will be my last posting to phys-l 'til July. I'm emotionally drained
by this experience, and a coauthor across town deserves much more of
my time. I'm going to immerse myself in optics for a while, and I'm
going to get outside more often. If you have a question for me please
direct it to my email address (leigh@sfu.ca) rather than my usual
return address. It will get looked at there.

Shalom,

Leigh

*with respect to angles only, of course.

Leigh Hunt Palmer                                  Phone: 604 291 4844
Department of Physics                                FAX: 604 291 3592
Simon Fraser University                             Home: 604 299 3731
Burnaby, BC  V5A 1S6                              email: leigh@sfu.ca
CANADA                                              122d58m W 49d17m N