A related problem is what appears to me to be a lack of clarity, both in the
mirror and lens equation, and in the ray diagrams used to show the formation
of images in typical textbooks, e.g., Serway.
The equation 1/p + 1/q = 1/f could be more easily understood by students if
they recognize that these three terms are angles. So, forget for now
distances p, q, f and concentrate on angles P=1/p, Q =1/q, F=1/f (this
latter is used as strength of lens in diopters).
Next, call diverging angles (as from a real object) NEGATIVE
Next write a logical equation:
original condition + change = final condition
or
(object angle) + (change due to lens) = (image angle)
-P + F = Q
which is equivalent to the traditional:
-(1/p) + (1/f) = (1/q)
In other words, concentrate on converging and diverging properties of the
rays.
This may not make much difference for a single lens or mirror, but it makes
problems involving 2 or 3 elements much easier to follow.
As for the ray diagrams: do ray diagrams of point objects situated on the
axis.
A real object will send diverging rays in the form of a sideways vee <. At
a converging lens, the convergence of the lens will either:
1 -bend the rays strongly inwards, towards the axis, >, forming a real image
2 - bend the rays slightly inwards, so they come out parallel
3 -bend the rays very slightly inwards, so they still diverge, but less than
originally, so the image is virtual.
Again, this procedure is useful when determining images due to two lenses, a
lens and mirror, etc.
The only disadvantage is that you cannot obtain the magnification from the
diagram.
Fouad Ajami
Physics Department
Champlain College
St Lambert, Qc, Canada
Tel: 450-672-7360-272
Fax: 450-672-7299