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. Each problem in the table 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 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 iz M RV I/NI Side +21 C, 9.3 9.3 C, 7.7

An object is placed 12 cm in front of a convex mirror of radius 40 cm. Find the position and magnification of the image. State whether the image is real or virtual, and draw a light ray diagram to show the image.

Consider the compound optical system shown in the diagram, where two thin lenses of focal lengths 7.5 cm (left lens) and 35 cm (right lens) are separated by a distance 25 cm.     If a 2.9 cm tall object is placed as indicated in part (a), and the image formed is 0.74 cm tall, what is the magnification of the first lens?  M1 =  b. Using the information from part (a), calculate the image distance, in centimeters, from the first lens.  di1 =

An astronomer orients two plane mirrors at an angle of 0, = 57.5° to each other, as shown below. He then directs a horizontal laser beam toward Mirror 1. The beam reflects twice: first off Mirror 1, then Mirror 2. What angle 0, will the outgoing beam make with the surface of Mirror 2? (Enter your answer in in degrees.) Mirror 1 Mirror 2