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[Phys-L] Re: PHYS-L Digest - 9 Aug 2005 to 10 Aug 2005 (#2005-253)



Chuck Britton wrote:

Please, when 'doing' ray diagrams, include MORE rays than the
requisite 'principal' rays.

The principal rays are only 'special' because we can do the geometry
with them easily.

I think that it is important to emphasize that ALL rays that share
the same origin as the principal rays do - will end up at the same
point as do all of the principle rays.
It's awful easy to JUST do the principle rays - and this sometimes
makes these rays seem overly 'special' or somehow the 'only' rays
that behave in this manner.

I understand Chuck's point, but I think there is a problem with much
instruction in this area. We have one faculty member who (years ago)
made the error of teaching by constructing only two principal rays,
the ones which pass through* the object point and the two focal
points of the lens. Of course they do intersect, but that is a most
unremarkable property of two lines drawn in a plane. This teacher
then alleged that intersection of the rays was at the position of the
image of the off axis object point and moved on. Of course that is
correct, but it should not be convincing to the student; certainly
nothing has been proved. It is only after the third principal ray
(the central ray) has been plotted that the remarkable property of
off axis imaging begins to emerge from the construction. When three
constructed rays intersect it should be emphasized that this is
remarkable. Chuck's fourth and fifth rays cannot be constructed using
the simple on axis imaging property (or at least I don't know how to
do it), but it is more believable that these rays might also
intersect in the same image point.

After constructing this in the abstract one should examine the
physical interpretation in considerable detail, something not done in
many text books, I'm afraid. In particular, I object to the common
practice of producing the "real image" by projecting it on a screen!
Clearly it is better to place the observer on the optical axis
looking back in the direction from which the rays come. The observer
will perceive an image as though an object existed at that place.
Placing a screen injects an unnecessary and evidently confusing
element into the physical system, and it leads the student to place
undue emphasis on the meaningless (but easily assessed) concepts of
"real" and "virtual" images. When I interact with students one on one
or in small groups I always have them look at a real image directly,
without a screen. This can often be done by placing a small object on
an overhead projector and having the student look "backwards" toward
the projection lens. This demonstration has produced many "aha"
moments. (It should be done in a brightly lit room or else the image
is too bright to look at.) After the image has been perceived in this
way a screen can be inserted at the image position. While the screen-
in configuration is more common, it is not easier to understand than
the simpler no-screen configuration.

In my opinion students should also be told, with emphasis, that this
is a thin lens model, one that works exceedingly well for such
lenses, and one that is applicable to much more complex lens
combinations as well. However, it is only an approximate
representation of physically realizable lenses. Real lens design
requires ray tracing to be done using Snell's law for many rays
originating at many different points on an extended object and
incident at many different points on the first surface of the lens
system. Images of each object point are only approximately common
points of intersection of these rays, and the tighter the group
formed by these rays in the image, the better the imaging property.
While real lens design is done using digital computers to draw ray
diagrams, there is much to be learned by extending the analytical
models considerably, and what can be learned informs the design of
real lenses as well.

Leigh

*Yes, I do mean pass through. Lines are infinite in extent. This is a
geometrical construction, not a concrete apparatus. Ray diagrams are
not suitable for the student who has no ability to abstract.