Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/section-a/1/solution

For two equal lenses with a virtual intermediate object, use positive distances for real objects on a lens's incident side and real images on its outgoing side. The first lens gives , hence . At the second lens these rays are already converging toward a point to its right: its object distance is therefore .
Thus the final image is real, to the right of lens 1. Its transverse magnification is : it is inverted. The intermediate focus is not a real object placed before lens 2.
Figure 1.
Two converging lenses and a real image
. Original paraxial ray construction with an arbitrary small object height. Two rays meet at the calculated inverted final image; dashed continuations show where lens 1 alone would have focused them. Details.

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