(Solved): Two-lens systems. In the figure, stick figure \( \mathrm{O} \) (the object) stands on the common ce ...

Two-lens systems. In the figure, stick figure \( \mathrm{O} \) (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 \( p_{1} \). Lens 2 is mounted within the farther boxed region, at distance \( d \). 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 \( \mathrm{C} \) or \( \mathrm{D} \) 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 \( i_{2} \) 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 \( \mathrm{O} \) or noninverted, and (e) on the same side of lens 2 as object \( O \) or on the opposite side.