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