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Re: My Optics Education Project (MOEP)




On Friday the 14th Paul Camp writes about what happens if we cover up half a
lens. Perhaps this question illustrates both why students have trouble with
physics and why society places little value on learning physics. In this case
the physics teacher teaches that you block half the light. This is what
would happen if you took (for example) a simple lens, split it in half, and
inserted an opaque material through half the lens. In the real would this
is unlikely to happen and of little practical value. If on the other hand
one takes a camera lens and blocks the top half with a piece of cardboard
one does in fact block out the top half of the image. Having observed this
some smart person (who probably had not had a physics course and so had a free
mind) concluded that photographs which included land and sky could be
improved by producing filters which were half clear and half grey (or yellow,
red, etc. for b&w) so that the light from the sky would be partially blocked
and the sky would not be so washed out in the picture.
I think that the difficulty with Physics is that most real world problems
are too complex to solve with simple Physics. The problem must be broken down
into a series of simple problems, the simple problems must be worked out, and
then the results must be integrated to produce a final solution. This
discovery was Galileo's contribution to Physics. However, few of our students
have ever had any previous experience with such multistep reasoning and it is
particularly difficult in physics because the simple models, when applied
naively, often yield results which make no sense or contradict our actual
experiences.

True enough but not exactly the problem I was addressing. To get to
the point you are noting here you have to lead the students to a
recognition that two (or more) lenses are necessarily more
complicated than one but you can start by building on the behavior of
one lens.

Goldberg and Mcdermott, Arons and others have noted that many
students labor under the belief that the three principle rays are
the only ones contributing to the formation of an image, a viewpoint
reinforced rather strongly by the fact that no textbook (to my
knowledge) ever shows any others playing a role. The point, then, is
to understand image formation by a single lens and then use that
knowledge to understand more complicated systems. Arons suggests
making them draw ray diagrams involving scads of rays going every
possible way. This tends to lead to some rather complicated and hard
to interpret pictures as you might imagine. Another approach, which
is what I suggested, is to systematically remove the principle rays
from consideration and force the student to consciously construct ray
diagrams to explain what they see when the principle rays clearly
cannot be involved. Cover up half the object (effectively what you
suggest above with the above camera experiment, which is not exactly
what I sugested -- wrong side of the lens); cover up half the lens on
the same side as the object; cover up half on the other side; mask
the lens with a circular cutout (now we're approaching camera
behavior); move the cutout off center; get another lens of smaller
diameter but the same focal length so that the object is bigger than
the lens. In each case, make a ray diagram that accounts for what you
see. Changes in brightness turn out to be an important clue to many
students (leading them to think loosely in terms of fewer rays which
suggests many more than just three rays involved).

Now after we see that the image is still there even when the lens is
not, we can approach multiple lens systems. You are quite correct and
perceptive in pointing out that a bright and photographically
inclined student might make this erroneous connection however it is
precisely that moment of cognitive dissonance that provides an
opportunity for figuring something out.

Sorry for the late reply. Been out of town for a while. Left work
behind.

Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29526 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
pjcamp@worldnet.att.org The Name of the Rose
(803)349-2227
fax: (803)349-2926