Two-lens systems. In the figure, 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 p1. Lens 2 is mounted within the farther boxed region, at distance d. For this problem, p1 = 8.4 cm, lens 1 is diverging, d = 15 cm, and lens 2 is converging. The distance between the lens and either focal point is 5.6 cm for lens 1 and 5.7 cm for lens 2. (You need to provide the proper sign). Find (a) the image distance iz 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 or virtual, (d) inverted from object O or noninverted, and (e) on the same side of lens 2 as object O or on the opposite side. (a) (b) (c) (d) (e) P1 Lens 1 d Lens 2 i2 M R/V 1/NI Side +8.4 D,5.6 15 C, 5.7 (a) Number Units (b) Number Units (c) (d) (e)An object is placed against the center of a thin lens and then moved 72 cm from it along the central axis as the image distance i is measured. The figure gives i versus object distance p out to p, = 48 cm. What is the image distance when p = 72 cm? 0 p (cm) i (cm) -10 -20 Number Units vSpherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is p, = +25 cm, the type of mirror is convex, and then the distance between the focal point and the mirror is 50 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) Number Units (b) Number i Units (c) Number Units (d) (e) (f) vIn the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation is d = 42.4 cm, measured along the central axis of the lens. The image is just 1/5 the size of the object. (a) What kind of lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens? Lens here Axis (a) (b) Number i Units v (c) Number i Units v