Chapter 33, Problem 106GP

The proper functioning of certain optical devices (e.g., optical fibers and spectrometers) requires that the input light be a collection or diverging rays within a·cone of half-angle θ (Fig. 33–50). If the light initially exists as a collimated beam (i.e., parallel rays), show that a single lens of focal length f and diameter D can be used to create the required input light if D/f = 2 tan θ. If θ = 3.5° for a certain spectrometer, what focal length lens should be used if the lens diameter is 5.0 cm?

FIGURE 33–50 Problem 106.