How Do You Calculate the Focal Lengths of Microscope Lenses?

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To calculate the focal lengths of the microscope lenses, the total length of the tube is 25.0 cm, and the overall magnification is 500, achieved by a 50x objective lens and a 10x eyepiece. The relevant equations involve magnification (m = H/h = -q/p) and the relationship between object distance (p), image distance (q), and focal length (f). The equations indicate that the sum of the focal lengths of the objective and eyepiece lenses equals the tube length. By setting up the equations for the two lenses, one can solve for the individual focal lengths. The challenge lies in correctly applying the equations to find the values for the objective and eyepiece lenses.
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Homework Statement



A microscope is made in a tube 25.0 cm long. It magnifies 5.00 x 10to the 2 times, 50.0 times by the objective lens and 10.0 times by the eyepiece. What are the focal lengths of the two lenses?


Homework Equations


m= H/h=-q/p
q= p(f) / p-f
H= -h(q/p)

The Attempt at a Solution


GIVEN m= 5.00 * 10 to the 2
REQUIRED f= focal length = ? cm is what i am trying to find
I don't think i have the right equation but i don't know which equation to use.
 
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u have got f-ob + f-eye = 25 cm...
Now...f-ob / f--eye = m

now u have two variables and two equations ...just solve it out...i couldn't get the later part of the question actually...
 

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