Chapter 35, Problem 57CP

Consider the lens–mirror arrangement shown in Figure P35.55. There are two final image positions to the left of the lens of focal length f_L. One image position is due to light traveling from the object to the left and passing through the lens. The other image position is due to light traveling to the right from the object, reflecting from the mirror of focal length f_M and then passing through the lens. For a given object position p between the lens and the mirror and measured with respect to the lens, there are two separation distances d between the lens and mirror that will cause the two images described above to be at the same location. Find both positions.