Re: understand understanding, simple explanations, etc.

[Leigh Palmer <palmer@sfu.ca>]

At 4:26 PM -0800 2/10/98, Rick Tarara wrote:

> It's still not clear to me what topics you feel can be covered with say
> Junior High School students or 'liberal-arts' Freshmen in College (many of
> whom, at least in the U.S., don't have the barest introduction to Calculus
> and have poor to non-existent graphical comprehension skills).  I'll let Ken
> explain rainbows without math since he cited it as an example of what he
> does but having rejected C&J and S&F he can probably save his breath, as far
> as you're concerned.

I would certainly do the easy things that are usually done, and I would
add more astronomy than is traditional. You have correctly judged my
challenge, of course. For that reason, and because I would answer your
question about what to teach, I'll let you in on my approach to the
rainbow. Rats! I thought the challenge was a good one, too.

You note that neither C&J nor S&F explains why red is on the outside
and blue (well, violet) is on the inside of the rainbow. I would teach
my less mathematically adept students how the rainbow is formed, but I
would do it using a couple of demonstrations and graphical aids, and I
would not have more than that one topic as a desired learning outcome
for that lecture.

I will assume that refraction itself has been learned. I would start
with a demonstration of Newton's phenomenon of colors, the dispersion
of white light using a prism to form a vividly colored spectrum using
the light from an overhead projector. Yes, this can be done easily* by
anyone who has grasped the concepts necessary to understanding the
phenomenon, though I have seen even teachers struggle with the task of
doing it. Having done this (and explained it using a diagram) I would
demonstrate minimum deviation by rotating the prism, emphasizing the
observation that it means that the rays of any given wavelength (which
in this case corresponds to color) deviate at approximately the same
angle over a considerable range of prism orientations**. The graphic
aids (diagrams and graphs) should be prepared in advance and copies
given to the students. If you have prisms of different glasses these
might be used; we have only dense flint prisms. Next I use a florence
flask filled with water and a slide projector to produce a colored
display which is not nearly so colorful as the prism, but which is
convincing (I hope) nonetheless. More graphics, discussion of higher
order bows, time for questions. A couple of nice slides would help,
and of course the handout with the graphics should include reference
to the standard books on the topic.

Having said all that, I must confess to you that I have never given
this lecture, but I would love to be asked to do so. The prescribed
curriculum for the courses I teach never permits this kind of time to
be devoted to such an unimportant topic as the rainbow. I get paid to
teach the curriculum, or at least to try to do so.

Leigh

* Don't expect great brilliance or width in the projected spectrum.
You should be able to calculate what can be expected. A higher
dispersion display can be produced with a diffraction grating if you
wish to show one.

** This is the point that is omitted from most explanations. It is
absolutely essential to grasping the rainbow concept.