LENSES

The main impact geometrical optics has had on mankind is through the use of lenses in microscopes, telescopes, eyeglasses, and of course, the human eye. The basic idea behind the construction of a lens is Snell’s law, but as our analysis of light reflected from a spherical raindrop indicated, we can get complex results from even simple geometries like a sphere. Modern optical systems like the zoom lens shown in Figure (1) are designed by computer. Lens design is an ideal problem for the computer, for tracing light rays through a lens system requires many repeated applications of Snell’s law. When we analyzed the spherical raindrop, we followed the paths of 12 rays for an index of refraction for only yellow light. A much better analysis would have resulted from tracing at least 100 rays for the yellow index of refraction, and then repeating the whole process for different indices of refraction, corresponding to different wavelengths or colors of light. This kind of analysis, while extremely tedious to do by hand, can be done in seconds on a modern desktop computer.
In this chapter we will restrict our discussion to the simplest of lens systems in order to see how basic instruments, like the microscope, telescope and eye, function. You will not learn here how to design a color corrected zoom lens like the Nikon lens shown below.

Figure 1: Nikon zoom lens.