Re: ray tracing assumptions

[Wolfgang Rueckner <rueckner@FAS.HARVARD.EDU>]

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> I have been following this discussion of ray tracing with interest.  I
> only use ray diagrams roughly to scale for students to approximately
> locate images as a check on calculations, and as a means to understand
> the general pattern of images for concave & convex lenses and mirrors.
>  I do not use them with multiple lens systems as are being discussed
> since I can see no easy way to produce the needed rays for the 2nd
> optical element to make quick and simple ray diagrams possible.  All of
> the calculations and discussions so far confirms that I do not want to
> do multiple lens/mirror ray diagrams.  For those systems calculations
> will suffice. If anyone knows an easy way to do this that students can
> do fairly quickly, I would like to see it.
> James Mackey

Since I now think I've learned how to explain this, I'll take a stab at it.

(1)  Pretend the second lens isn't there and draw the three rays from
the object to the first lens and continue on to the image, but keep
in mind that there are an infinite number of these rays which
originate from the same point on the object and converge on the
corresponding point on the image.  You can sketch in a goodly number
of these rays since you now know from the first three rays where they
should be headed.  (I even like to shade in the diverging cone of
rays from the object and the cone converging on the image.)

(2)  Put the second lens back in the set-up.  The image is no longer
where you have indicated it should be in part (1), but you DO know
the direction all those rays are headed in as they strike the second
lens.  Pick out the appropriate ones from this bundle of sketched
rays that you know how to deal with (the focal, parallel, and or
center ray) vis a vis the second lens and follow them through the
second lens.  Now use them to locate the image.

Wolfgang