Having issues with this compound lens problem

Question

I am having trouble finding the focal length of the objective lens in this problem.

The barrel of a compound microscope is 16.2 cm in length. The specimen will be mounted 1.11 cm from the objective, and the eyepiece has a 5.20 cm focal length. Determine the focal length of the objective lens.

Answer 1

Seems like you need more information in order to do the problem. Usually, you have 4 pieces of info for the compound microscope (like magnification or f_o = d_o,o). Here you're trying to solve for f_o sol you can't assume that the object is at the focal length. However, you can do this for the eyepiece and using the near point:

Assume that m_e = 25 cm/f_e = 4.8077

Now you can assume that the magnification for the eyepiece is correct, but the positioning is such that the real image cast by the objective will be positioned inside the focal length of the eyepiece so that d_i,e/d_o,e = m_e that we have approximated. (All length in cm)

d_i,e = - 4.8077d_o,e

You can now solve for d_o,e: 1/f_e = 1/d_o,e - 1/(4.8077d_i,e)

Once you have this, you can solve for f_o: 1/f_o = 1/d_o + 1/(16.2-d_o,e) (both do and di are positive for objective and the image is real, inverted, and magnified)

I get 1.017 cm which is close to 1.11 cm

Take care and please consider a tutor.