5. A diverging thin lens and a concave mirror have focal lengths of equal magnitude. An object is placed f from the diverging lens, and the mirror is placed a distance 3f on the other side of the lens. Using Gaussian optics, determine the final image of the system, after TWO refractions (a) by a three-ray diagram (drawn to scale), and (b) by calculation. (Pedrotti 2-22)- see diagram. 6. A clear crystal bead of index 1.720, and radius 1.50 cm is submerged in a clear liquid of index 1.360. If a parallel beam of light in the liquid is allowed to enter the bead, at what point beyond the other side will the light be brought to a focus? [Jenkins & White 3.15]. 7. A small object is placed 20 cm from the first of a train of THREE lenses with focal lengths, in order, of 10, 15, and 20 cm. The first TWO lenses are separated by 30 cm and the LAST TWO by 20 cm. Calculate the final image position relative to the last lens and its linear magnification relative to the original object when a) All THREE lenses are positive, b) The middle lens is negative, c) The first and last lenses are negative. Also draw ray diagrams (drawn to scale) for each case. (Pedrotti 2-23) 8. Determine the ratio of focal lengths for two identical, thin, plano-convex lenses when one is silvered on its flat side and the other on its curved side. Light is incident on the unsilvered side. [Pedrotti 2-30]. 9. We now use the three lenses in question (5) part (b) above, but the lenses are placed in contact to form a single compound lens instead. a) Find the powers of the individual lenses and that of the combined unit, in diopters. b) Find the vergence of an object point 20 cm from the combined unit, and that of the resulting image. Convert the image distance to centimeters.