Problem 2 - Combined Thin Lenses (10 points) A thin convex lens of focal length of 30 cm and a thin concave lens of focal length of 20 cm are placed 20 cm apart from each other. An upright object is placed 40 cm in front of the convex lens. 40 cm oe om f, = 30cm f, = -20cm (a) Using a ray diagram and thin lens equations sketch and calculate the position of the image. (5 points) (b) What is the transverse magnification of the system? (1.5 points) (c) What is the longitudinal magnification of the system? (Longitudinal magnification is defined as the magnification of an object in the direction parallel to the optical axis, and is multiplicative for multi-element systems: M; = My; - Mj). (1.5 points) (d) What are the front and back focal lengths of the combined lens system? (2 points) Round all results to one decimal place