Figure 4.16: To calculate the combined optical power of a chain of lenses, the algebra is simple: Add their diopters. This arrangement of four lenses is equivalent to a $ 6$-diopter lens, which has a focal length of $ 0.1667$m.

For optical systems used in VR, several lenses will be combined in succession. What is the effect of the combination? A convenient method to answer this question with simple arithmetic was invented by ophthalmologists. The idea is to define a diopter, which is $ D = 1/f$. Thus, it is the reciprocal of the focal length. If a lens focuses parallel rays at a distance of $ 0.2$m in behind the lens, then $ D = 5$. A larger diopter $ D$ means greater converging power. Likewise, a concave lens yields $ D < 0$, with a lower number implying greater divergence. To combine several nearby lenses in succession, we simply add their diopters to determine their equivalent power as a single, simple lens. Figure 4.16 shows a simple example.

Steven M LaValle 2020-01-06