Ray Tracing

In practice, it is often instructive to trace the paths of light rays as they traverse a lens system. Ray tracing can provide a helpful check on computations based on the vergence equation. For a thin convex lens in air, it is convenient to depict the source object as a vertical arrow, with its tail on the optic axis and its head at a distance—say, h—from the optic axis. We take a central vertical line to be the common location of the front and back principal planes. The ray from the tail of the arrow through the center of the lens on the optic axis passes undeviated. To locate the image of the arrow, we can trace 2 rays that originate at the tip of the arrow. The ray that propagates parallel to the optic axis is bent at the common principal plane and passes through the back focal point, F2. The ray from the tip of the arrow through the front focal point, F1, is bent at the common principal plane and redirected to continue parallel to the optic axis, where it eventually crosses the (refracted) path of the previous ray, locating the image of the tip of the arrow. In general, we can also use a third ray, from the tip of the arrow through the (common) principal point on the optic axis (the “center” of the lens) to confirm the construction. By symmetry, this ray will emerge from the lens as if undeviated (though in fact it makes a slight zigzag as it enters and exits the lens) and should also intersect the point of intersection of the previous 2 rays (see Fig 1-17).

The various cases of interest with the source object arrow located at different distances from a thin convex lens, at the front focal point, and between the front focal point and the lens are illustrated in Figure 1-19. The ray tracing for a thin concave lens in air is shown in Figure 1-20.

Figure 1-19 Ray tracing for a simple convex lens in air. The blue arrow represents a movable object; the green arrow shows the corresponding image location and size. Points F1 and F2 are the front and back focal points of the lens, respectively. A, Source object far to left; real image (inverted and minified) is on opposite side of lens. B, Source object at left, near first focal point; real image (inverted and enlarged) is on opposite side of lens. C, Source object coincides with first focal point; “image” is at infinity. D, Source object between first focal point and lens; virtual image (upright and enlarged) is seen to left of source object.

(Illustration developed by Scott E. Brodie, MD, PhD.)

Figure 1-20 Ray tracing for a concave lens in air. The blue line represents a movable object; the green line shows the corresponding image location and size. A, Source object at left. Virtual image, minified, lies between focal point and the lens. B, Moving the object between focal point and lens produces similar virtual image, though with less image minification.

(Illustration developed by Scott E. Brodie, MD, PhD.)

Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.