Re: Diffraction

[Cliff Parker <cparker@EMPOWERING.COM>]

>  "What happens when we have three coherently derived
> waves?"

Perhaps I have the wrong idea about what happens in diffraction (wrong ideas are
not uncommon in my head) but isn't the pattern of energy, and the lack there of,
a result of not two, three or even four or five coherently derived waves but
rather the result of virtually an infinite number of waves all converging at the
same time?  In other words isn't this phenomenon calculus in action?  If I do
have things right here, then I think that my students can be shown graphically
the results of two independent waves as they interfere with each other, and then
stretch their imaginations to see the results of many, many, many, waves all
operating together to form the visible effect.  When I describe something like
this I do tell students that if they ever want to more fully work with these
ideas they will have to learn the calculus (I teach an algebra/trig based
physics). Some of them will.  I hear from those in calc. class as the year goes
by about those lessons that they can now apply to things we have studied in the
past.  Some of the other students may at least have a glimpse of just what the
more advanced math is all about, and yes, I have to admit a few can muster up
only a blank stare.

> The problem of the rainbow is a similar one. If you look at the
> "explanations" provided in high school textbooks you will see that
> they aren't explanations at all. All they say is that light is
> reflected and refracted within raindrops. Given such explanations a
> student couldn't tell you whether red shows up on the outside or
> the inside of a rainbow, and he wouldn't have a clue how to calculate
> the angular size of the bow.

You have me here.  I must confess I do not fully understand the problem of the
rainbow and I tell my students so, because you can be sure they will ask at some
time during the year.  I do not let my lack of explanation prevent them from
observing, wondering about and appreciating a rainbow.

> Both phenomena should be seen by and discussed in high school (and
> even earlier) science classes. It doesn't matter that they can't be
> explained. If we exclude the unexplained from their experience what
> can we expect them to have to look forward to?

Once again, good point.  If these are shown early in a students scientific
experience, however, I think the explanation from the teacher should be "You
will find out later," or more likely "I don't know myself but someday I hope to
find out.  Maybe you will be the one to teach me."  If the best the teacher can
do is read and spit back the books explanation he or she should refrain from
doing so.

> I love teaching in
> university because whenever something really interesting of a
> scientific nature occurs in the news, I get to tell my students
> about it. It doesn't matter that I might not be able to explain it.
> If it is scientifically interesting (if I'm interested) then I
> share it with them, with or without explanation. Say the Higgs is
> produced. I don't understand what that means; I certainly can't
> explain it to my students, but I sure would let them know about it.

What makes you think that a person must teach in the university to be able to
share such things with students?  My students are, for the most part, the only
people I can talk to about such things with any degree of comprehension or
interest.  We discuss Bose-Einstein Condensate for example, they have to sit
still long enough for me to explain the little bit that I know and open the door
to the great deal I don't know.  At least that gives enough information for us
to chew on for a while.

Cliff Parker