Chapter 35, Problem 31P

You are working for an electronics company that makes devices for the home. Your supervisor has given you an assignment to help design the projection mechanism for a projection alarm clock. In this type of clock, a projection system is mounted on the body of the clock, as shown in Figure P35.31a, where the projection system is the silver cylinder, of radius R = 3.25 cm, mounted on the left side of the clock. A converging lens is mounted on the edge of the cylinder. Inside the cylinder, a small digital display of the time in red characters can be moved from the center of the cylinder outward radially toward the lens. The red light of the digital display can he seen in the lens in Figure P35.31a. As a result, an image of the time is projected in red onto the ceiling or wall of a darkened room (Fig. P35.31b). The range of distances for focused images of the digital display is from 0.500 m to 4.00 m, measured from the center of the cylinder. For the smallest value of the range, the digital display is at the center of the cylinder. You must determine for your supervisor the following parameters for the design of the projection system: (a) the focal length of the lens and (b) the distance of the digital display from the center of the cylinder for the largest value of the range.

Figure P35.31