Halliday, Resnick & Walker — Images: Problem 58 through 65

58 through 65 Two-lens systems. In Fig. 34-35, stick figure O (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to O, which is at object distance \( p_1 \). Lens 2 is mounted within the farther boxed region, at distance \( d \). Each problem in Table 34-7 refers to a different combination of lenses and different values for distances, which are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance \( i_2 \) for the image produced by lens 2 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final image is (c) real (R) or virtual (V), (d) inverted (I) from object O or noninverted (NI), and (e) on the same side of lens 2 as object O or on the opposite side. Table 34-7 Values: 58: \( p_1 = +10, \text{Lens 1} = C, 8.0, d = 30, \text{Lens 2} = D, 8.0 \) 59: \( p_1 = +20, \text{Lens 1} = D, 12, d = 10, \text{Lens 2} = D, 8.0 \) 60: \( p_1 = +18, \text{Lens 1} = C, 12, d = 67, \text{Lens 2} = C, 10 \) 61: \( p_1 = +12, \text{Lens 1} = C, 8.0, d = 32, \text{Lens 2} = C, 6.0 \) 62: \( p_1 = +12, \text{Lens 1} = C, 15, d = 10, \text{Lens 2} = C, 8.0 \) 63: \( p_1 = +20, \text{Lens 1} = C, 9.0, d = 8.0, \text{Lens 2} = C, 5.0 \) 64: \( p_1 = +10, \text{Lens 1} = D, 6.0, d = 12, \text{Lens 2} = C, 6.0 \) 65: \( p_1 = +4.0, \text{Lens 1} = C, 6.0, d = 8.0, \text{Lens 2} = D, 6.0 \)