Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: ray tracing assumptions

I don't agree with this. Mirror ray diagrams have the virtue that
you're always dealing with real light rays traveling in the direction
of the propagation of the light. Thus, even if the image from the
first mirror is a virtual image and resides behind the mirror (where
there's really no light at all), it doesn't matter conceptually
because the light rays you are dealing with have bounced off that
mirror and are heading towards the next mirror in an easily
understood direction -- they're coming from the direction of that
virtual image. They could of course also be coming from a real image
in front of the mirror.

But in the case of lenses, one runs into a conceptual problem when
trying to draw ray diagrams that you don't run into with mirrors. I
think that you and John Denker are sweeping this issue under the rug
in your reply. Maybe it would help to give a specific lens
configuration:

When a lamp is placed 42 cm to the left of a particular convex lens,
suppose a real (inverted) image is formed 37.5 cm to the right of the
lens. The lamp and convex lens are kept in place while a concave
lens is mounted 15 cm to the right of the convex lens. A real image
of the lamp is now formed 35 cm to the right of the concave lens.
What is the focal length of each lens?

Applying the lens equation to the convex lens, one obtains +19.8 cm.
Applying the lens equation again to the concave lens (using the image
of the convex lens as the object of the concave lens), one obtains
-63 cm. But one runs into a conceptual issue (which I tried to
explain in my first query) if you try to draw the ray diagrams for
this situation. Try it!

The only answer I've come up with is that you can't solve a problem
by drawing ray diagrams when the object of a lens is a virtual object
-- that is to say, the object is on the same side of the lens in
which the light is headed. To put it another way, you can only draw
the diagrams using rays which are headed in the real direction of the
propagation of light. That conclusion may seem obvious, but I've
never heard that rule nor seen it in any textbook.



It sounds to me as if your only problem is explaining the concept
of a "virtual object." You seem to imply that mirrors avoid ever
having to deal with virtual objects, but that is not the case.

Irrespective of the identity of the optical element, when its
"input rays" are converging, we say it is processing the light of
a "virtual object." The optical element doesn't care about that,
it just processes the rays. If the element is a converging lens
or a concave mirror, then the output rays are *more* strongly
convergent. If it is a diverging lens or a convex mirror, then
the output rays are *less* strongly convergent and possibly even
divergent.

I find that these kinds of difficulties are much more easily dealt
with if one emphasizes the vergence properties of input and output
rays rather than the locations of images and objects. The latter
are necessary, of course, but they should be treated merely as
*tools* that help one to determine the vergence properties of the
rays, *not* vice-versa.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

On Wed, 17 Apr 2002, Wolfgang Rueckner wrote:

I would like to know how phys-l people answer the following common
student question when it comes to ray tracing in optics. The
question arises from any number of lens combinations, but let's keep
it simple and consider the case of two convex lenses in contact with
each other. One can calculate the effective or combined focal length
of the combination by applying the lens equation (using the
appropriate sign conventions for object, image, and focal length
distances) to the first lens, on which the light is incident, and
then again to the second lens but using the image of the first as the
object of the second. Now, students often ask why it is that we can
> treat the image of the first lens as the object of the second when,
in fact, the image is not where we're pretending it is (because the
second lens is actually in the way).

Let me contrast this to ray tracing with mirrors, in which case this
objection doesn't arise. That is, when we have a mirror combination,
we use the image of the first mirror (be it real or virtual) as the
object for the second mirror without any conceptual problems because
the light rays from the first mirror are really coming from the
direction of the image it has produced. For lens combinations,
however, that's not the case because the presence of the second lens
doesn't let the rays from the first lens converge where we're
pretending the image is -- yet we ignore that, pretend it's there
> anyway, and then go on to use that image which isn't there as our
> object for the next lens. Yet the method works! Have any of you had
> similar student questions about this and how do you answer them?
Looking forward to your insights -- Wolfgang