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Re: Diffraction



I have the radical opinion that an explanation of the effects
should not be attempted until it can be approached with appropriate
mathematics, and that is beyond high school in most cases. The
students should still be introduced to the phenomena, but it should
not be necessary to "explain" them in some lame fashion crippled by
the lack of the right tools.

Convince me. How will the ideas of wavefronts composed of infinite numbers
of point sources interfering with each other both constructively and
destructively, and the effect on such interference's as these wavefronts
passes through slits going to harm my students? Two slit diffraction of
light is one of my, and my students, favorite topics of contemplation. It
seems to me that not a great deal of mathematics is required to understand
that waves will superimpose onto each other and constructively and
destructively interfere with each other given differing path lengths. How
can I get students to appreciate the dual nature of light without some
understanding of what is happening in diffraction and the fact that this
phenomenon is unique to waves? Should I teach such a wondrous concept in
the same way that scientific method is too often introduced, as a set of
facts to be remembered but not comprehended? Too many students leave high
school physics classes knowing that light behaves as a wave and a particle
but not understanding or even considering that such a thing is absolutely
ridiculous. What good is it to even introduce diffraction (or any other
physical phenomenon) if no explanation is to be offered?

The phenomenon of two slit "diffraction" is usually called the Young's
double slit experiment, a demonstration of the wave nature of light,
but seldom called "diffraction". It is most easily explained by
considering the interference of two coherently derived point sources.
I think that demonstration of the effect with light and repeating it
in a ripple tank are the best ways to show students the behaviour of
waves. The graphical construction of the explanation of interference
is also fair game at the high school level, but don't expect the
students to be able to generalize; don't expect they will do much with
the problem of "What happens when we have three coherently derived
waves?" And don't expect anything but blank stares when you present
them with what is usually called a diffraction problem, say the single
slit. I can certainly wave my hands to explain that pattern, too, and
I confess that I have done so. I don't believe I taught anyone
anything when I did so without putting the mathematics behind it.

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.

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? 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.

I love to play with magnets. I can buy small, cheap, very powerful
magnets at a yuppie hardware store here in Vancouver. I show them
to many visitors, including my three year old granddaughter Elizabeth.
Kids are fascinated by them. Of course they'd love to know how they
work, but I certainly can't tell them. Still, there are things I can
do with magnets that I can sort of explain. E.g. take two identical
rubber refrigerator magnets. Put them face to face and rub one across
the other. Vary the relative orientation of the two and try rubbing
again. You'll find something interesting, which I can explain in terms
of things that happen with the little magnets, but I can't explain the
little magnets' behaviour to an elementary school student. Should I
withhold the very attractive phenomena from them for that reason?

Leigh