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Ray Tracing
Ray tracing is the graphical solution to problems with thin lenses aka geometric optics. Given a single,
double, or any number of thin lenses, one can follow this simple procedure to achieve a satisfactory
solution. Basically all of these problems are about locating the final image given an object and a (set of)
lens (lenses).
A single thin convex lens is always a good start. Suppose the lens has a focal length of 10 cm and an
object is 20 cm from the lens. The goal is to find the image – i.e. where does the image of this object
appear? Since all visible objects reflect light, in all directions, the choice of which reflected light rays is
key. In almost all of these problems the same three are chosen so as to facilitate a simple process for
locating the final image.
Selected light rays:
1) parallel to the horizontal,
2) through the center of the lens, and
3) through the focal length on the same side as the object.
A picture is worth a thousand words – so see Fig. 1.
Fig. 1. Ray Tracing for a Single Convex Lens
Each ray interacts at the center of the lens. This approximation is why the lens is described as “thin”. With
a thick lens one would have to apply Snell’s law in order to determine how that ray bends through the
glass. However, in this case that is not a problem since the lens is thin and the light bends at the center.
The thing to remember is how much the rays bend:
1) the parallel ray passes through the focal point on the other side of the lens,
2) the straight through ray passes – straight through the lens, and
3) the focal length ray passes through the lens parallel to the horizontal axis.
NOTE: ray 1 and ray 3 are the opposites of each other. This is in fact an example of a very good principle
to know in optics. It is called optical reversibility. Whatever a ray does in one direction, then if you
reverse the direction of that ray, it will have the same path as before.
Finally for this lecture supplement is the single thin concave lens. In this case the rays take a different
route. The bend away from each other so as to diverge. See Fig. 2.
Fig. 2. . Ray Tracing for a Single Concave Lens
NOTE: the lenses can easily remembered by seeing the concave lens as having a “cave” shape. Then the
convex lens is the other one.
Just one other thing – since the rays for the convex lens come together it is also referred to as a
converging lens; whereas the concave lens is also referred to as a diverging lens.