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 30cm and the last two by 20cm. 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. Provide ray diagrams for each case.

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 30cm and the last two by 20cm. 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. Provide ray diagrams for each case.