focal length in single lens, length of camera

Question

A telephoto lens consists of a combination of a converging lens and a diverging lens placed at a certain distance from each other. This enables us to produce a large image of a distant object with a single lens combination in a camera. We want to use a telephoto lens to take an action shot of a football game. The converging lens is of focal length 12 cm, and the diverging lens is of focal length – 6 cm, both separated by a distance of 8cm. If the action is 100 m away, find the position of the final image and the magnification of the system. What focal length would be necessary in a single lens to produce an image of the same size? How long has the camera to be?

Answer 1

The combined focal length of system of two lenses is 36cm of convex lens

1/F =1/f1+1/f2 - d/f1*f2

for f= 36 cm v = 0.372 m Real diminished inverted image

magnification = I/O = 100/0.372

for single convex lens focal length is to be 37 cm