Microscope objectives and eyepieces are often labeled simply with a magnification. A 5x eyepiece and a 21x objective result in a total magnification of 105x for the system. Assuming these are simple converging lenses and the objective is brought to a distance of 8.6 mm from the specimen, what focal lengths are needed for the eyepiece and the objective to give the 105x system magnification? (Assume that the specimen is placed just outside the focal length of one of the lenses. Include the sign of the value in your answers.)

Microscope objectives and eyepieces are often labeled simply with a magnification. A 5x eyepiece and a 21x objective result in a total magnification of 105x for the system. Assuming these are simple converging lenses and the objective is brought to a distance of 8.6 mm from the specimen, what focal lengths are needed for the eyepiece and the objective to give the 105x system magnification? (Assume that the specimen is placed just outside the focal length of one of the lenses. Include the sign of the value in your answers.)